2017"百度之星"程序设计大赛

度度熊保护村庄

Accepts: 47

Submissions: 900

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 32768/32768 K (Java/Others)

Problem Description

哗啦啦村袭击了喵哈哈村！

度度熊为了拯救喵哈哈村，带着自己的伙伴去救援喵哈哈村去了！度度熊与伙伴们很快的就过来占据了喵哈哈村的各个军事要地，牢牢的守住了喵哈哈村。

但是度度熊发现，这是一场旷日持久的战斗，所以度度熊决定要以逸待劳，保存尽量多的体力，去迎战哗啦啦村的战士。

于是度度熊决定派尽量多的人去休息，但是同时也不能松懈对喵哈哈村的保护。

换句话而言，度度熊希望尽量多的人休息，而且存在一个包围圈由剩下的人组成，且能够恰好的包围住喵哈哈村的所有住房（包括边界）。

请问最多能让多少个人休息呢？

Input

本题包含若干组测试数据。

第一行一个整数n，表示喵哈哈村的住房数量。

接下来n行，每行两个整数(x1[i],y1[i])，表示喵哈哈村的住房坐标。

第n+1行一个整数m，表示度度熊的士兵数量。

接下来m行，每行两个整数(x2[i],y2[i])，表示度度熊伙伴的坐标。

满足:

1<=n,m<=500

-10000<=x1[i],x2[i],y1[i],y2[i]<=10000

Output

请输出最多的人员休息的数目。

如果无法保护整个村庄的话，输出"ToT"

Sample Input

2
1 1
2 2
4
0 0
0 4
4 2
4 0
1
1 1
2
0 0
0 1

Sample Output

1
ToT
这题没思路先放这55555555。
----------------------跟新线----------------------
题解请点击这里
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度度熊的王国战略

Accepts: 674

Submissions: 6056

Time Limit: 40000/20000 MS (Java/Others)

Memory Limit: 32768/132768 K (Java/Others)

Problem Description

度度熊国王率领着喵哈哈族的勇士，准备进攻哗啦啦族。

哗啦啦族是一个强悍的民族，里面有充满智慧的谋士，拥有无穷力量的战士。

所以这一场战争，将会十分艰难。

为了更好的进攻哗啦啦族，度度熊决定首先应该从内部瓦解哗啦啦族。

第一步就是应该使得哗啦啦族内部不能同心齐力，需要内部有间隙。

哗啦啦族一共有n个将领，他们一共有m个强关系，摧毁每一个强关系都需要一定的代价。

现在度度熊命令你需要摧毁一些强关系，使得内部的将领，不能通过这些强关系，连成一个完整的连通块，以保证战争的顺利进行。

请问最少应该付出多少的代价。

Input

本题包含若干组测试数据。

第一行两个整数n，m，表示有n个将领，m个关系。

接下来m行，每行三个整数u,v,w。表示u将领和v将领之间存在一个强关系，摧毁这个强关系需要代价w

数据范围：

2<=n<=3000

1<=m<=100000

1<=u,v<=n

1<=w<=1000

Output

对于每组测试数据，输出最小需要的代价。

Sample Input

2 1
1 2 1
3 3
1 2 5
1 2 4
2 3 3

Sample Output

1
3

最小割问题，可惜不懂，不过这题数据很水，只要求与其他将领强关系总和最小的那个将领完全分割出来就行。可以用并查集，肯定只有一个集合才可以分割，如果有两个集合就说明已经分开来了，答案就是0了。

#include <iostream>
#include <stdio.h>
#include <string.h>
#include <vector>
#include <map>
#define ll long long
using namespace std;
const int N=1e5+10;
map<int,int>mp1,mp;
int fa[2*N], n,m;
vector<int>vs[N];
int find(int x) {
    if(x==fa[x])
        return x;
    return fa[x]=find(fa[x]);
}
int edge[3010][3010];
void unite(int x,int y) {
    x=find(x);
    y=find(y);
    if(x != y) {
        fa[x] = y;
    }
}
void init() {
    for(int i = 1; i <= n; i ++) {
        vs[i].clear();
        fa[i] = i;
    }
    memset(edge, 0, sizeof(edge));
    mp1.clear();
    mp.clear();
}
inline int read() {
    int x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
int main(){
    while(scanf("%d%d",&n,&m) != EOF){
        init();
        for(int i = 1; i <= m; i ++){
            int s, t, w;
            s = read(); t = read(); w = read();
            if(edge[s][t]) {
                edge[s][t] += w;
                edge[t][s] += w;
            }else {
                edge[s][t] = w;
                edge[t][s] = w;
            }
            unite(s,t);
        }
        for(int i = 1; i <= n; i ++) {
            for(int j = 1; j <= n; j ++) {
                if(i == j) continue;
                mp1[i] += (edge[i][j]);
            }
        }
        for(int i = 1; i <= n; i++) {
            if(mp[find(i)]) {
                mp[find(i)]=min(mp[find(i)],mp1[i]);
            }else {
                mp[find(i)]=mp1[i];
            }
            vs[find(i)].push_back(i);
        }
        ll ans = 0;
        for(int i=1;i<=n;i++){
            if(find(i)==i){
                if(vs[i].size()>1){
                    ans += mp[i];
                }
            }
        }
        printf("%lld
",ans);
    }
    return 0;
}

度度熊与邪恶大魔王

Accepts: 3666

Submissions: 22474

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 32768/32768 K (Java/Others)

Problem Description

度度熊为了拯救可爱的公主，于是与邪恶大魔王战斗起来。

邪恶大魔王的麾下有n个怪兽，每个怪兽有a[i]的生命值，以及b[i]的防御力。

度度熊一共拥有m种攻击方式，第i种攻击方式，需要消耗k[i]的晶石，造成p[i]点伤害。

当然，如果度度熊使用第i个技能打在第j个怪兽上面的话，会使得第j个怪兽的生命值减少p[i]-b[j]，当然如果伤害小于防御，那么攻击就不会奏效。

如果怪兽的生命值降为0或以下，那么怪兽就会被消灭。

当然每个技能都可以使用无限次。

请问度度熊最少携带多少晶石，就可以消灭所有的怪兽。

Input

本题包含若干组测试数据。

第一行两个整数n，m,表示有n个怪兽，m种技能。

接下来n行，每行两个整数，a[i],b[i]，分别表示怪兽的生命值和防御力。

再接下来m行，每行两个整数k[i]和p[i]，分别表示技能的消耗晶石数目和技能的伤害值。

数据范围:

1<=n<=100000

1<=m<=1000

1<=a[i]<=1000

0<=b[i]<=10

0<=k[i]<=100000

0<=p[i]<=1000

Output

对于每组测试数据，输出最小的晶石消耗数量，如果不能击败所有的怪兽，输出-1

Sample Input

1 2
3 5
7 10
6 8
1 2
3 5
10 7
8 6

Sample Output

6
18
完全背包问题。
设dp[i][j]为生命值为i防御为j的怪物最少需要多少晶石消灭。那么每个怪物要消灭的最少晶石在里面查下就行了，注意是长整数。

#include <iostream>
#include <stdio.h>
#include <string.h>
#define ll long long
using namespace std;
const int N = 100010;
const int M = 1010;
ll a[N], b[N], p[M], k[M];
ll dp[M][12];
int main() {
    int n, m;
    while(scanf("%d %d", &n, &m) != EOF) {
        ll ans1 = 0, ans2 = 0, ans3 = 0;
        for(int i = 1; i <= n; i ++) {
            cin >> a[i] >> b[i];
            ans1 = max(ans1, a[i]);
            ans2 = max(ans2, b[i]);
        }
        for(int i = 1; i <= m; i ++) {
            cin >> k[i] >> p[i];
            ans3 = max(ans3, p[i]);
        }
        if(ans3 <= ans2) {
            printf("-1
");
            continue;
        }
        for(int i = 0; i < M; i ++) {
            for(int j = 0; j < 12; j ++) dp[i][j] = 100000000000L;
        }
        for(int i = 0; i < 12; i ++) dp[0][i] = 0;
        for(int i = 1; i <= m; i ++) {
            for(int j = 1; j <= ans1; j ++) {
                for(int l = 0; l < 12; l ++) {
                    if(p[i] <= l) continue;
                    int ans = p[i]-l;
                    if(ans >= j) dp[j][l] = min(dp[j][l], dp[0][l]+k[i]);
                    else dp[j][l] = min(dp[j][l], dp[j-ans][l]+k[i]);
                }
            }
        }
        ll sum = 0;
        for(int i = 1; i <= n; i ++) {
            if(a[i] <= 0) continue;
            sum += dp[a[i]][b[i]];
        }
        printf("%lld
",sum);
    }
    return 0;
}

度度熊的午饭时光

Accepts: 823

Submissions: 9241

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 32768/32768 K (Java/Others)

Problem Description

度度熊最期待每天的午饭时光，因为早饭菜品清淡，晚饭减肥不敢吃太多（胖纸的忧伤T.T）。

百度食堂的午餐超级丰富，祖国各大菜系应有尽有，度度熊在每个窗口都有爱吃的菜品，而且他还为喜爱的菜品打了分，吃货的情怀呀(>.<)。

但是，好吃的饭菜总是很贵，每天的午饭预算有限，请帮度度熊算一算，怎样打饭才能买到的最好吃的饭菜?(不超过预算、不重样、午餐等分最高的情况下，选择菜品序号加和最小，加和相等时字典序最小的组合)

Input

第一行一个整数T，表示T组数据。 每组测试数据将以如下格式从标准输入读入：

B

N

score_1 cost_1

score_2 cost_2

:

score_N cost_N

第一行，正整数B（0 <= B <= 1000），代表午餐的预算。

第二行，正整数N (0 <= N <= 100)，代表午餐可选的菜品数量

从第三行到第 (N + 2) 行，每行两个正整数，以空格分隔，score_i表示菜品的得分，cost_i表示菜品的价格(0 <= score_i, cost_i <= 100)。

Output

对于每组数据，输出两行： 第一行输出："Case #i:"。i代表第i组测试数据。 第二行输出菜品的总得分和总花费，以空格分隔。 第三行输出所选菜品的序号，菜品序号从1开始，以空格分隔。

Sample Input

2
29
6
9 10
3 4
6 5
7 20
10 9
15 11
0
2
2 23
10 12

Sample Output

Case #1:
34 29
2 3 5 6
Case #2:
0 0

01背包问题，就是处理序号问题麻烦点，在分数最高的情况下，只有不超过预算，那个取序号和最小的，如果相同求字典序最小的。dp[i]表示花费为i最大可获取的分数，当dp[j] < dp[j-cost[i]] + sco[i]时
肯定把dp[j-cost[i]]里的序号和i全放在dp[j]里,相同时就让dp[j]里的序列号和或字典序与dp[j-cost[i]]和i的序列号和或字典序比较了。

#include <iostream>
#include <stdio.h>
#include <string.h>
#include <vector>
#include <algorithm>
using namespace std;
const int N = 1100;
const int M = 1010;
int cost[N], sco[N], dp[M], c[N];
vector<int> vs[M], tmp;
void init() {
    for(int i = 0; i < M; i ++) vs[i].clear();
    memset(cost, 0, sizeof(cost));
    memset(sco, 0, sizeof(sco));
    memset(dp,0,sizeof(dp));
}
char a[N], b[N];
void check(int x, int y, int p) {
    memset(a, 0, sizeof(a));
    memset(b, 0, sizeof(b));
    int sum1 = 0, sum2 = 0, len1 = vs[x].size(), len2 = vs[y].size();
    for(int i = 0; i < len1; i ++) {
        sum1 += vs[x][i];
        a[i] = vs[x][i]-'0';
    }
    for(int i = 0; i < len2; i ++) {
        sum2 += vs[y][i];
        b[i] = vs[y][i] - '0';
    }
    sum2 += p;b[len2] = p - '0';
    if(sum1 > sum2) {
        tmp.clear();
        for(int i = 0; i < len2; i ++) {
            tmp.push_back(vs[y][i]);
        }
        tmp.push_back(p);
        vs[x].clear();
        for(int i = 0; i < tmp.size(); i ++) {
            vs[x].push_back(tmp[i]);
        }
    }else if(sum1 == sum2) {
        sort(a, a+len1); sort(b, b+len2+1);
        if(strcmp(a,b) > 0) {
            tmp.clear();
            for(int i = 0; i < len2; i ++) {
                tmp.push_back(vs[y][i]);
            }
            tmp.push_back(p);
            vs[x].clear();
            for(int i = 0; i < tmp.size(); i ++) {
                vs[x].push_back(tmp[i]);
            }
        }
    }
}
bool check1(int x, int y) {
    memset(a, 0, sizeof(a));
    memset(b, 0, sizeof(b));
    int sum1 = 0, sum2 = 0, len1 = vs[x].size(), len2 = vs[y].size();
    for(int i = 0; i < len1; i ++) {
        sum1 += vs[x][i];
        a[i] = vs[x][i] - '0';
    }
    for(int i = 0; i < len2; i ++) {
        sum2 += vs[y][i];
        b[i] = vs[y][i] - '0';
    }
    if(sum1 < sum2) {
        return true;
    } else if(sum1 == sum2) {
        if(strcmp(a, b) < 0) {
            return true;
        }
    }
    return false;
}
int main() {
    int t, cas = 1;
    cin >> t;
    while(t--) {
        init();
        int b, n;
        cin >> b >> n;
        for(int i = 1; i <= n; i ++) cin >> sco[i] >> cost[i];
        for(int i = 1; i <= n; i ++) {
            for(int j = b; j >= cost[i]; j --) {
                if(dp[j] < dp[j-cost[i]] + sco[i]) {
                    // printf("%d
",dp[j]);
                    dp[j] = dp[j-cost[i]] + sco[i];
                    tmp.clear();
                    for(int k = 0; k < vs[j-cost[i]].size(); k ++) {
                        tmp.push_back(vs[j-cost[i]][k]);
                    }
                    tmp.push_back(i);
                    vs[j].clear();
                    for(int k = 0; k < tmp.size(); k ++) {
                        vs[j].push_back(tmp[k]);
                    }
                }else if(dp[j] == dp[j-cost[i]] + sco[i]) {
                    check(j,j-cost[i],i);
                }
            }
        }
        int MC = 0, MSCo = 0;
        for(int i = 0; i <= b; i ++) {
            if(dp[i] > MSCo) {
                MSCo = dp[i];
                MC = i;
            } else if(dp[i] == MSCo) {
                if(check1(i, MC)) {
                    MC = i;
                }
            }
        }
        printf("Case #%d:
",cas++);
        printf("%d %d
",MSCo, MC);
        memset(c, 0, sizeof(c));
        int cnt = 0;
        for(int i = 0; i < vs[MC].size(); i ++) {
            c[cnt++] = vs[MC][i];
        }
        sort(c, c+cnt);
        for(int i = 0; i < cnt; i ++) {
            printf("%d%c",c[i],(i == (cnt-1) ? '
': ' '));
        }
    }
    return 0;
}

寻找母串

Accepts: 211

Submissions: 2019

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 32768/32768 K (Java/Others)

Problem Description

对于一个串S，当它同时满足如下条件时，它就是一个01偏串： 1、只由0和1两种符组成； 2、在S的每一个前缀中，0的个数不超过1的个数； 3、S中0的个数和1的个数相等。

现在给定01偏串S，请计算一下S在所有长度为n的01偏串中作为子串出现的次数的总和。 由于结果比较大，结果对1e9+7取余后输出。

样例解释： 在第二个样例中，长度为4的偏串共两个1010，1100。10在1010中出现了两次，在1100中出现了1次。所以答案是3。

Input

第一行给出一个整数T(1<=T<=40),表示测试数据的数目。 每一组测试包含一个整数n和字符串S，中间用空格分开。(1<=|S|<=100000，1<=n<=1000000000)

输入保证S是一个01偏串。

Output

对于每一组数据，输出一个整数占一行，表示答案。

Sample Input

2
2 10
4 10

Sample Output

1
3

有规律，规律就是

但是n是1e9，这么大肯定不好求了。而51nod里的1120题目也是求大数组合的，那个可以用卡特兰数+卢卡斯定理，不过卢卡斯定理的求模不能超过1e5，所以这个可以用卡特兰数来算。

不懂的请自行百度卡特兰数，直接丢公式。

f(n)表示对n个卡特兰数只需把上面的规律变成C(n,2n)的形式就行了。

令(n-|s|)/2+1=x，所以上面的规律就是C(x,2x-1)=C(x,2x)/2 =f(x)*(n-1)/2

现在只要求出f(x)就行了，卡特兰数有个递推公式，f(x)=2(2x-1)f(x-1)/(x+1),但是x最大有5e8，那么我们可以打表，每隔10万计一下数每次输入一组数据后求出x，然后x/100000求出它是第几个10万卡特兰数，在用递推公式算下第x个卡特兰数就行了，除法要用乘法逆元表示。这个打表打了5千个。0.0

#include <iostream>
#include <algorithm>
#include <string.h>
#include <stdio.h>
#define ll long long
using namespace std;
const int N = 1000100;
const ll mod = 1e9+7;

ll cat[N] = {1 , 945729344, 874271714, 728937729, 488957151, 213941567, 621948608, 165410919, 130152966, 477849061, 70646122, 104331417, 804334677, 112228257, 406385851, 373610584, 959189339, 129232103, 596011761, 653302265, 502350404, 254254274, 23933464, 200023312, 437339905, 838455202, 353529507, 181826790, 268707842, 918554769, 361346624, 475114772, 551764204, 264122255, 348587014, 339775734, 190610810, 147039338, 576212642, 958452888, 907080272, 897468755, 485757524, 926001334, 253159604, 720502565, 795701677, 485379561, 512490195, 62869610, 44647373, 170729326, 181183678, 223602264, 14266485, 546070015, 669748641, 266401585, 722432477, 844276843, 806809752, 215407850, 514089950, 48258832, 388402233, 287386547, 184275733, 39087220, 221157750, 796058916, 274451201, 551481903, 468840632, 654694122, 349643823, 123450237, 466554578, 613371117, 104229634, 534520804, 340376885, 53768135, 665006362, 362834988, 113383960, 458629513, 877935697, 990187981, 24010351, 477599350, 491321663, 619368665, 730486899, 302800222, 248364522, 617385859, 136706557, 988949479, 681384128, 140672609, 39443745, 327846413, 353172956, 108275948, 378351259, 482275913, 432213793, 904945283, 871063203, 757590126, 541675614, 649654378, 339103071, 153511190, 307061975, 535998427, 953278988, 315396128, 629843192, 166102135, 623766767, 9922024, 962639966, 258645380, 484156059, 75913669, 837794293, 574075634, 404396328, 768092500, 903633183, 512519672, 44285819, 538902069, 621789723, 71341556, 81438997, 28847533, 40513591, 849551327, 716939958, 942552133, 395636757, 409774346, 383255288, 612104482, 95851638, 696370843, 884779483, 524922348, 220269701, 390881347, 114227221, 395767320, 614338019, 380172060, 180822541, 691300228, 891829295, 967678016, 701386253, 162940737, 994175698, 908221589, 19098271, 438672588, 631720803, 573850469, 339056525, 473356393, 859071294, 949727021, 98529638, 168890563, 563975847, 7483795, 276476730, 39489314, 514728211, 87529508, 963753157, 380031470, 856696972, 158703490, 515908206, 227044626, 959511111, 993078622, 80360936, 888779384, 323285665, 543535546, 550763954, 601069950, 458756853, 717452438, 141044757, 197501322, 634124805, 238583278, 200414323, 553793080, 66504653, 42069842, 722598090, 913608032, 740683059, 742050754, 961341417, 612741304, 91785690, 526087340, 214299335, 290988315, 920349511, 650032143, 826861662, 655676777, 832872230, 243503280, 428075391, 780176613, 762279490, 958553222, 298583588, 683539087, 245173409, 561149407, 172900450, 994863083, 373712992, 577710034, 676813275, 65061172, 354158163, 474587452, 779048700, 252731521, 513247255, 63716789, 589280106, 300449755, 843219077, 437936157, 617131692, 778975010, 166446598, 341293627, 939851882, 377019792, 974135048, 18159888, 617899054, 824539871, 922256819, 904951680, 298436189, 877366713, 763013330, 69488053, 73161945, 968841940, 502298660, 815060335, 585478837, 52225572, 617841877, 964952304, 864682249, 537138023, 438032312, 507344261, 611203109, 211965075, 510592131, 253042462, 662211654, 306668985, 993054101, 886017682, 550897294, 748379779, 600811784, 662510825, 923914254, 398819263, 459843924, 563578785, 800110936, 890507874, 833696238, 67588077, 662523469, 355339772, 897895240, 326276953, 66185485, 707119691, 543399352, 359252814, 343020869, 435649016, 326479513, 313711009, 180736295, 933688638, 341979700, 832484396, 852821336, 938966456, 327938691, 897898594, 514258765, 67631305, 832209634, 147167201, 933864871, 764372915, 290610995, 894446445, 552066969, 955550128, 899538317, 98587581, 791520663, 371485442, 250166899, 386277652, 850700239, 24883422, 365069578, 542759096, 393648297, 338311897, 998392022, 963038213, 184331347, 216025562, 616142588, 243671535, 922469047, 642896156, 173840546, 617065897, 502916270, 399859525, 626708892, 203438585, 794335044, 466847771, 485435744, 176762177, 370414892, 387922877, 421040690, 506803021, 831791096, 536761402, 659624740, 205742555, 354512880, 992080290, 655638247, 441557017, 45234385, 602453687, 642559130, 907907516, 150309994, 959349261, 667245533, 336984599, 7514180, 293021893, 527065808, 716061908, 183191397, 64976751, 577967909, 833760679, 814950379, 238991246, 714290102, 902231891, 437427307, 149073027, 103173270, 685925477, 694198173, 725256565, 71168984, 261760780, 55757530, 112359206, 436686978, 516723667, 537954237, 916255072, 34043384, 456908325, 881291767, 146092388, 189805926, 498850664, 471576564, 977024064, 502710283, 230937450, 166248501, 100683033, 725464484, 750575586, 525293805, 107750423, 541103694, 100780834, 184498203, 767490572, 317419646, 113029816, 182757677, 138614676, 694365799, 832641460, 450632411, 301670090, 972578606, 809851941, 356139480, 741575534, 319109663, 491688831, 946837771, 820876500, 944731056, 441691410, 439779726, 878100434, 110259934, 781810231, 822737100, 122949140, 185157201, 147977057, 78103215, 98159640, 570747872, 913214189, 526507036, 614910594, 606219102, 234699129, 882201646, 184318349, 623751699, 220799331, 756153289, 390599249, 416019375, 679472812, 608212465, 946818526, 676784388, 848462543, 701625645, 631586665, 279738981, 507735946, 983863013, 797150469, 667058957, 302361878, 11123699, 265956565, 759232458, 630434107, 603234456, 651468455, 184824418, 604726700, 101186449, 24954474, 873710205, 172883575, 299713548, 965606121, 589841373, 782619807, 545740664, 94087806, 846145323, 99057958, 275906334, 98324641, 712417499, 506415720, 153372884, 988856645, 995466415, 137196894, 296743168, 461577383, 447394859, 350928543, 800328411, 359672375, 623997509, 289025167, 258422311, 586168764, 714133593, 295537278, 650382172, 140783549, 886171581, 956390396, 255289567, 255216580, 795608020, 678371829, 996937306, 387496328, 235100473, 649738138, 898466097, 407604566, 529571196, 854241604, 278302571, 998505802, 446819056, 674284500, 819876855, 166920818, 141076505, 198714798, 612486167, 700718656, 391542764, 645522969, 999548402, 477521930, 505594128, 951413460, 665706996, 664760847, 514065631, 101412856, 896853242, 846607158, 200777626, 574295366, 319187233, 35082951, 154276754, 661540946, 477502005, 725521461, 655895869, 355739306, 678518235, 192498927, 173855439, 165487057, 456827891, 29739781, 258791510, 428391536, 531278508, 763339063, 168419466, 868466779, 365442496, 722700915, 698024831, 661694896, 590895521, 463918561, 314021483, 842517461, 302478861, 688035954, 232366905, 961113387, 828397927, 320767088, 508824951, 735431855, 426624942, 591154618, 76109991, 328101502, 665849594, 385026767, 472223460, 891042862, 342446307, 246096980, 406346591, 527916773, 998217449, 259406947, 423766371, 70821164, 405777406, 55383694, 177073358, 520289379, 953144123, 598695706, 882910945, 148088957, 127593638, 565277379, 746539154, 329767227, 652704430, 458041013, 532152689, 943689273, 198275398, 746095184, 296234153, 567962117, 585755152, 914398975, 392347020, 605551281, 526603889, 299409566, 554048889, 207398267, 231395425, 761907727, 542580836, 511879608, 477430193, 68337675, 420520000, 90537136, 881957003, 293703031, 601859481, 982488742, 687784417, 778652850, 678832519, 41785321, 569973809, 659662535, 165782945, 800601868, 946694094, 798296737, 530957874, 155643917, 78799254, 840622486, 223970795, 8485824, 28964502, 945323929, 340741737, 34732972, 603272702, 607664609, 673843887, 72927622, 72008879, 956047483, 777700919, 664146374, 919751340, 24878865, 460990642, 148315028, 357424860, 741503968, 317099797, 829104947, 566163262, 167156841, 600465821, 697110956, 353280563, 96899824, 252662837, 7893272, 120921870, 514991140, 889565398, 248085788, 692098208, 933756018, 425884820, 645876939, 21896522, 887680365, 852291368, 441176290, 66262852, 156844282, 636816511, 124116038, 842190463, 966404243, 788403295, 940665695, 989549719, 828820601, 250027891, 298842711, 270122615, 174406628, 2135753, 46964343, 877722285, 279439798, 165618275, 192058083, 45442983, 312364959, 141906913, 672563513, 989170139, 871761564, 190705367, 121151650, 442674415, 781847041, 760092753, 473161041, 775211615, 133246058, 75660748, 105103896, 314024082, 699785781, 135093763, 341755252, 356922254, 545665155, 516050961, 683432858, 554252611, 980150710, 3809442, 280205936, 618138190, 143338978, 788688497, 335020131, 301878323, 399780697, 432488867, 731503292, 78552686, 970031600, 634518684, 501384623, 44760617, 805930887, 940017151, 197445475, 720089820, 203297800, 544488568, 323817708, 248584685, 735890324, 467669218, 62087980, 905110436, 891634369, 10533152, 23990287, 611609572, 542849349, 924481418, 4214140, 12444440, 736717687, 401040098, 157325666, 367265798, 451303368, 161946117, 507226623, 459380345, 866752949, 897212880, 806566311, 378612676, 64109037, 642588978, 48895787, 519942317, 136434876, 29861018, 573535950, 758513856, 146511954, 726260224, 399742173, 745185429, 190644678, 862659605, 284303510, 93481167, 54655028, 557236856, 907886262, 184073171, 469064478, 587825128, 561305691, 650561892, 494974250, 427901529, 127482682, 377916374, 510109927, 601476427, 61867544, 242080407, 336520612, 817284238, 357107802, 831433550, 401060931, 360517611, 209089633, 445727073, 273046955, 399724590, 819481328, 852463455, 937507966, 711938640, 599907247, 439538485, 872938446, 909790292, 180096711, 650114586, 529418274, 560890330, 882019804, 509410348, 501169449, 344529911, 730231156, 858736987, 621110787, 4459667, 873347202, 696188165, 506145206, 73642136, 147943559, 379421898, 654783213, 956981417, 651743441, 639780318, 78577382, 593374499, 830162763, 301755654, 792435305, 117970707, 932913412, 832255341, 132217712, 628450721, 227843471, 107653574, 884405265, 36919433, 120185702, 713929739, 355335147, 939617354, 
    328252980, 400671521, 3750430, 291712420, 161768446, 204525632, 110812455, 655316736, 810170496, 495246572, 411585803, 110977744, 480012790, 837775503, 421678299, 537576259, 215096702, 255249918, 999498556, 551932245, 400608941, 789747750, 660573311, 224129758, 960267908, 823407521, 663185418, 71834349, 194653367, 479377667, 556838543, 30135513, 434301805, 554957759, 766164228, 423757881, 77024851, 446918481, 86585877, 167204113, 199048610, 165982142, 29904724, 116697346, 136404554, 840462862, 989156366, 172584177, 788447557, 850533198, 955155103, 112270248, 718115841, 395066112, 581133650, 802794769, 427918059, 178030850, 977926539, 732960431, 699231435, 65702561, 976789228, 525323070, 86516285, 991883842, 476155672, 748102517, 322281052, 655855568, 406512465, 964314311, 364509254, 195333797, 846194973, 949738561, 886254842, 502143379, 589271740, 437138529, 387943507, 470570144, 725480162, 669584085, 390652246, 75608046, 254775915, 749807458, 399204577, 389518587, 676947848, 716992238, 919341531, 597635407, 280866713, 144960231, 434116773, 916307902, 416987077, 890332575, 250543518, 711290749, 609117110, 101790252, 341587080, 760344158, 527693811, 318500054, 328492483, 720790022, 212571117, 361377324, 531509358, 751847974, 886497431, 858449169, 934013125, 788050176, 850699702, 248810880, 44441799, 642211420, 705573309, 24708499, 697713950, 120454565, 987670705, 829805968, 155043798, 809295463, 198062340, 220732544, 344473911, 880492204, 2038436, 944738188, 276417253, 611404975, 432855654, 786086830, 154324346, 797055600, 81184023, 352392093, 78560743, 769267534, 188623471, 891873067, 597600944, 635025615, 228156015, 549216704, 38864598, 63700934, 642477540, 375302266, 953440571, 962793031, 282043806, 539322985, 25446468, 117648763, 169455125, 120897864, 87881494, 545841159, 771895116, 136580960, 157187855, 776017848, 962707012, 39503440, 910505941, 614200021, 949980263, 915287649, 666122087, 746726358, 34334955, 352453528, 993894309, 483994924, 554577132, 632653418, 231205736, 526017288, 531492304, 858186711, 658185632, 437684486, 388797172, 87656439, 143442048, 977222510, 51584599, 676403054, 21887037, 310923006, 569449572, 657178857, 87893014, 437053905, 104461171, 554450666, 43805303, 795485481, 873115631, 247594776, 770261640, 330356539, 152552771, 437835910, 140803358, 470347487, 409255424, 679123739, 102757226, 735832872, 881201701, 977704789, 997586222, 224007165, 273193389, 457636155, 92154325, 448813997, 857983852, 42617141, 742134656, 65964759, 531393281, 17238319, 830087579, 254323836, 723445009, 930990624, 479255983, 91551188, 65774342, 279563516, 679097326, 179469301, 702743798, 929427653, 814434172, 330288556, 211704567, 283074416, 262054775, 754010164, 776761179, 132845418, 534231538, 34229724, 195970213, 657800241, 755172561, 364070929, 365961326, 741172323, 376852198, 395396933, 968033538, 477416299, 564491661, 709283428, 489509922, 905330548, 723541522, 780759864, 134664756, 792724815, 963896303, 567528866, 844166935, 169392541, 680577839, 171914778, 957909749, 211668514, 82957327, 44234607, 117590458, 440473834, 620784373, 14157720, 451003384, 983615836, 874696072, 778532988, 476571600, 265345981, 698792583, 280038803, 329624138, 151695003, 111941196, 514504079, 820758255, 233110954, 664754899, 137441315, 570223850, 194965848, 360409182, 739091511, 33239113, 935173903, 390436161, 424186967, 393517525, 153598984, 33444950, 996562973, 747116784, 475741089, 388402463, 123164340, 252744207, 45683619, 286149821, 151352219, 253348457, 141215346, 266674334, 955441001, 567007829, 395176771, 77581436, 856850141, 544290627, 30091875, 849950577, 392214186, 201596847, 789966079, 291632986, 634087056, 367465808, 923890692, 714154326, 96395067, 14462136, 673997336, 58048965, 143620650, 986057005, 738602909, 676856554, 262658375, 881073550, 735766624, 101600085, 562793177, 755867698, 611633641, 83001444, 555445968, 840211632, 962912697, 536127393, 413177670, 629812280, 144402004, 895312763, 483303557, 617554985, 377341180, 919868020, 224757310, 692354129, 338976285, 123095596, 925293996, 134174250, 705551158, 390400479, 514039691, 44359150, 258684627, 710602795, 306364191, 381736861, 627472181, 656170231, 931322351, 120602560, 691837679, 187119332, 16726777, 202984091, 56859736, 48373380, 741653736, 154736306, 941819960, 244682436, 810153781, 438809981, 10776833, 798074778, 738964379, 722270935, 527866427, 35177978, 868149794, 690506771, 13188734, 33748791, 759403473, 332684799, 759456692, 400505841, 651619221, 305211078, 306719869, 49600531, 284379031, 698176697, 271698007, 295342551, 406973798, 753021319, 976471593, 261940372, 12785345, 124617930, 221763912, 683402006, 382633811, 883800246, 730897031, 776117466, 60563, 149264352, 869189868, 111356869, 953749071, 722568957, 819523770, 800957876, 929322647, 528022127, 874685768, 603082478, 934748494, 976933172, 892528229, 556869197, 636890668, 608745675, 416733789, 648416081, 952212514, 95308692, 619065966, 771370365, 706486874, 752557136, 391766815, 601217911, 207014632, 873793506, 903755102, 968664489, 860177742, 817393859, 656227158, 194791064, 224321827, 532160944, 339449269, 752532971, 181868455, 154128541, 723960722, 62582671, 656504834, 728970183, 769911353, 685725527, 731596785, 243125725, 710401534, 491533761, 146158067, 27223577, 635248711, 487608280, 894138759, 791657460, 167681185, 682741956, 509525358, 678807444, 365157513, 563896167, 178771924, 176282538, 278986827, 360384478, 795358537, 322958119, 70396395, 458025298, 583881289, 677075893, 949791975, 126071912, 137383873, 884309528, 718365207, 496976979, 73359019, 994058135, 696948974, 343517950, 790345044, 221559459, 331808088, 342748895, 465970642, 693958964, 936344042, 98179810, 191785663, 699778777, 195483637, 124747596, 612777425, 442653810, 67413099, 881563022, 753626088, 610013081, 527753366, 891671548, 74863503, 588240560, 845937766, 261231314, 603200603, 975194516, 513474524, 994347975, 651575835, 501929355, 364699412, 617648981, 548491680, 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char str[N];
void exgcd(ll a, ll b, ll &x, ll &y) {
    if(!b){
        x = 1; y = 0;
    }else{
        exgcd(b, a%b, y, x);
        y -= x*(a/b);
    }
}    
ll inv(ll a, ll n) {
    ll x, y;
    exgcd(a, n, x, y);
    return (x+n)%n;
}   
ll pow_mod(ll x, ll n, ll mod){  
    ll res=1;  
    while(n>0){  
        if(n&1)res=res*x%mod;  
        x=x*x%mod;  
        n>>=1;  
    }  
    return res;  
} 
ll n;
int main() {
    int t;
    scanf("%d",&t);
    while(t--) {
        scanf("%lld%s",&n,str);
        // cin >> n >> str;
        ll len = strlen(str);
        if(n&1LL || n < len ) {
            printf("0
");
            continue;
        }
        ll x = (n-len)/2+1;
        ll index = x/100000;
        ll ans = cat[index];
        // printf("%lld
",ans);
        for(ll i = index*100000+1; i <= x; i ++) {
            // printf("%lld
",i);
            ans = (2*(2*i-1)*ans%mod*pow_mod(i+1,mod-2,mod)%mod)%mod;
            // printf("%lld %lld
",i,ans);
        }
        // printf("%lld
",ans);
        printf("%lld
",(((x+1)*ans)%mod*pow_mod(2,mod-2,mod)%mod)%mod);
    }
    return 0;
}