第八场多校联盟 Problem D: 数列问题 【矩阵快速幂】

Description

一个数列数列f(0)=0,f(1)=1,f(2)=1,f(3)=2,f(4)=3,f(5)=5......

Input

输入整数t,表示t组测试数据

接下来t行,每行输入n(0<n<1000000000000)

Output

对于每个n输出f(n)%1000007

Sample Input

2
1
3

Sample Output

1
2

#include <cstdio>
#include <iostream>
using namespace std;

const long long MOD = 1000007;

struct matrix
{
long long m[2][2];
}ans, base;

matrix multi(matrix a, matrix b)
{
matrix tmp;
for(long long i = 0; i < 2; ++i)
{
for(long long j = 0; j < 2; ++j)
{
tmp.m[i][j] = 0;
for(long long k = 0; k < 2; ++k)
tmp.m[i][j] = (tmp.m[i][j] + a.m[i][k] * b.m[k][j]) % MOD;
}
}
return tmp;
}
long long fast_mod(long long n)
{
base.m[0][0] = base.m[0][1] = base.m[1][0] = 1;
base.m[1][1] = 0;
ans.m[0][0] = ans.m[1][1] = 1;
ans.m[0][1] = ans.m[1][0] = 0;
while(n)
{
if(n & 1)
ans = multi(ans, base);
base = multi(base, base);
n >>= 1;
}
return ans.m[0][1];
}
int main()
{
ios::sync_with_stdio(false);
long long number;
int t;
cin>>t;
while(t--)
{
cin>>number;
cout<<fast_mod(number)<<endl;
}

return 0;
}