Educational Codeforces Round 13 D. Iterated Linear Function 逆元+公式+费马小定理

D. Iterated Linear Function

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Consider a linear function f(x) = Ax + B. Let's define g(0)(x) = x and g(n)(x) = f(g(n - 1)(x))for n > 0. For the given integer values A, B, n and x find the value of g(n)(x) modulo 109 + 7.

Input

The only line contains four integers A, B, n and x (1 ≤ A, B, x ≤ 109, 1 ≤ n ≤ 1018) — the parameters from the problem statement.

Note that the given value n can be too large, so you should use 64-bit integer type to store it. In C++ you can use the long long integer type and in Java you can use long integer type.

Output

Print the only integer s — the value g(n)(x) modulo 109 + 7.

Examples

input

3 4 1 1

output

7

input

3 4 2 1

output

25

input

3 4 3 1

output

79

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <vector>
#include <queue>
#include <map>
#include <algorithm>
#include <set>
using namespace std;
#define MM(a,b) memset(a,b,sizeof(a))
#define SC scanf
#define PF printf
#define CT continue
typedef long long ll;
typedef unsigned long long ULL;
const int mod = 1000000007;
const double eps = 1e-10;
const int inf = 0x3f3f3f3f;
const int N=2*1e5+10;

ll quick(ll a,ll n)
{
    ll res=1;
    while(n){
        if(n&1) res=(res*a)%mod;
        a=(a*a)%mod;
        n>>=1;
    }
    return res;
}

ll yuan(ll n)
{
    return quick(n,mod-2);
}

int main()
{
    ll a,b,n,x;
    while(~SC("%lld%lld%lld%lld",&a,&b,&n,&x)){
        ll ans=0;
        ans+=quick(a,n)*x%mod;
        ans+=b*(quick(a,n)-1)%mod*yuan(a-1)%mod;
        PF("%lld
",ans);
    }
    return 0;
}

逆元求法：利用费马小定理

http://blog.csdn.net/qq_21057881/article/details/51758437