二项式定理+前缀Sigma

https://hihocoder.com/problemset/problem/1430

思路：

要用前缀去推Sigma总公式，比较方便。https://blog.csdn.net/weixin_37517391/article/details/83821752

#define IOS ios_base::sync_with_stdio(0); cin.tie(0);
#include <cstdio>//sprintf islower isupper
#include <cstdlib>//malloc  exit strcat itoa system("cls")
#include <iostream>//pair
#include <fstream>//freopen("C:\Users\13606\Desktop\草稿.txt","r",stdin);
#include <bitset>
//#include <map>
//#include<unordered_map>
#include <vector>
#include <stack>
#include <set>
#include <string.h>//strstr substr
#include <string>
#include <time.h>//and(((unsigned)time(NULL))); Seed n=rand()%10 - 0~9;
#include <cmath>
#include <deque>
#include <queue>//priority_queue<int, vector<int>, greater<int> > q;//less
#include <vector>//emplace_back
//#include <math.h>
//#include <windows.h>//reverse(a,a+len);// ~ ! ~ ! floor
#include <algorithm>//sort + unique : sz=unique(b+1,b+n+1)-(b+1);+nth_element(first, nth, last, compare)
using namespace std;//next_permutation(a+1,a+1+n);//prev_permutation
#define rint register int
#define fo(a,b,c) for(rint a=b;a<=c;++a)
#define fr(a,b,c) for(rint a=b;a>=c;--a)
#define mem(a,b) memset(a,b,sizeof(a))
#define pr printf
#define sc scanf
#define ls rt<<1
#define rs rt<<1|1
typedef long long ll;
void swapp(int &a,int &b);
double fabss(double a);
int maxx(int a,int b);
int minn(int a,int b);
int Del_bit_1(int n);
int lowbit(int n);
int abss(int a);
const double E=2.718281828;
const double PI=acos(-1.0);
//const ll INF=(1LL<<60);
const int inf=(1<<30);
const double ESP=1e-9;
const int mod=(int)1e9+7;
const int N=(int)5e4+10;

long long C[110][110];
void Init() {
    C[0][0] = 1;
    for(int i = 1;i <= 100;++i) {
        C[i][0] = 1;
        for(int j = 1;j <= i;++j) {
            C[i][j] = (C[i-1][j-1] + C[i-1][j]) % mod;
        }
    }
}
//======================================================Cnk预处理;
ll S[105][N],SS[105][N],ans[N];
char s[N];

void solve()
{
    ll n,k;
    sc("%lld%lld",&n,&k);
    sc("%s",s);

    for(int i = 0;i <= n;++i) S[0][i] = 1;
    for(int i = 1;i <= n;++i) S[1][i] = (s[i-1]-'0') + S[1][i-1] ;
    for(int i = 2;i <= k;++i)
        for(int j = 1;j <= n;++j)
            S[i][j] = S[1][j] * S[i-1][j] % mod;

    SS[0][0] = 1;

    for(int i = 0;i <= k;++i) {
        for(int j = 1;j <= n;++j)
            SS[i][j] = (SS[i][j-1] + S[i][j])%mod;
    }

    for(int i=1;i<=n;++i)
    {
        ll sum=0;
        for(int j=0;j<=k;++j)
        {
            ll temp=C[k][j]*S[k-j][i]%mod*SS[j][i-1]%mod;
            if(j&1)
                sum=(sum-temp+mod)%mod;
            else
                sum=(sum+temp)%mod;
        }
        ans[i]=sum;
    }
    for(int i=1;i<=n;++i)
        pr("%lld%c",ans[i],i==n?'
':' ');
}

int main()
{
    Init();
    int T;
    sc("%d",&T);
    while(T--)solve();
    return 0;
}

/**************************************************************************************/

int maxx(int a,int b)
{
    return a>b?a:b;
}

void swapp(int &a,int &b)
{
    a^=b^=a^=b;
}

int lowbit(int n)
{
    return n&(-n);
}

int Del_bit_1(int n)
{
    return n&(n-1);
}

int abss(int a)
{
    return a>0?a:-a;
}

double fabss(double a)
{
    return a>0?a:-a;
}

int minn(int a,int b)
{
    return a<b?a:b;
}