zoj3690 Choosing number 矩阵

Choosing number

And you need to calculate how many ways they can choose the numbers obeying the rule.

Input

There are multiple test cases. Each case contain a line, containing three integer n (2 ≤ n ≤ 10⁸), m (2 ≤ m ≤ 30000), k(0 ≤ k ≤ m).

Output

One line for each case. The number of ways module 1000000007.

Sample Input

4 4 1

Sample Output

216

#include<cstring>
#include<iostream>
using namespace std;
typedef long long ll;
const ll mod=1000000007;

struct matrix{
    ll f[2][2];
};

matrix mul(matrix a,matrix b){
    matrix s;
    memset(s.f,0,sizeof s.f);
    ll i,j,k;
    for(i=0;i<2;i++)
        for(j=0;j<2;j++)
    for(k=0;k<2;k++){
        s.f[i][j]+=a.f[i][k]*b.f[k][j];
        s.f[i][j]%=mod;
    }
    return s;
}

matrix pow_mod(matrix a,ll k){
    matrix s;
    s.f[0][0]=s.f[1][1]=1;
    s.f[0][1]=s.f[1][0]=0;
    while(k){
        if(k&1)   s=mul(s,a);
        a=mul(a,a);
        k>>=1;
    }
    return s;
}

int main(){
    ll n,m,k;
    while(cin>>n>>m>>k){
        matrix e;
        e.f[0][0]=e.f[1][0]=m-k;
        e.f[0][1]=k;
        e.f[1][1]=k-1;

        e=pow_mod(e,n-1);
        ll ans=((m-k)*e.f[0][0]+k*e.f[1][0]+(m-k)*e.f[0][1]+k*e.f[1][1])%mod;
        cout<<ans<<endl;
    }
    return 0;
}