UVaLive 7361（矩阵快速幂）

题意：矩阵快速幂求斐波那契数列。

分析：

#include<cstdio>
#include<cstring>
#include<cctype>
#include<cstdlib>
#include<cmath>
#include<iostream>
#include<sstream>
#include<iterator>
#include<algorithm>
#include<string>
#include<vector>
#include<set>
#include<map>
#include<deque>
#include<queue>
#include<stack>
#include<list>
#define fin freopen("in.txt", "r", stdin)
#define fout freopen("out.txt", "w", stdout)
#define pr(x) cout << #x << " : " << x << "   "
#define prln(x) cout << #x << " : " << x << endl
typedef long long ll;
typedef unsigned long long llu;
const int INT_INF = 0x3f3f3f3f;
const int INT_M_INF = 0x7f7f7f7f;
const ll LL_INF = 0x3f3f3f3f3f3f3f3f;
const ll LL_M_INF = 0x7f7f7f7f7f7f7f7f;
const double pi = acos(-1.0);
const double EPS = 1e-6;
const int dx[] = {0, 0, -1, 1};
const int dy[] = {-1, 1, 0, 0};
const ll MOD = 1e9;
const int MAXN = 1000 + 10;
const int MAXT = 10000 + 10;
using namespace std;
struct Node
{
    ll c[2][2];
    Node()
    {
        memset(c, 0, sizeof c);
    }
};
Node multi(Node &a, Node &b)
{
    Node ans;
    for(int i = 0; i < 2; ++i)
        for(int j = 0; j < 2; ++j)
            for(int k = 0; k < 2; ++k){
                ans.c[i][j] += (a.c[i][k] * b.c[k][j]);
                ans.c[i][j] %= MOD;
            }
    return ans;
}
ll q_pow(ll cur)
{
    Node a;
    a.c[0][0] = a.c[0][1] = a.c[1][0] = 1;
    Node ans;
    ans.c[0][0] = ans.c[1][1] = 1;
    while(cur)
    {
        if(cur & 1)
        {
            ans = multi(ans, a);
        }
        a = multi(a, a);
        cur /= 2;
    }
    return ans.c[0][0];
}
int main()
{
    int P;
    scanf("%d", &P);
    while(P--)
    {
        int K;
        ll Y;
        scanf("%d%lld", &K, &Y);
        printf("%d %lld\n", K, q_pow(Y - 1));
    }
    return 0;
}