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 <bits/stdc++.h>
long long mod = 1e9 + 7;
using namespace std;
ifstream fin("ciur.in");
ofstream fout("ciur.out");
long long lgp(long long a, long long b) {
  if (b == 0) return 1;
  long long k = lgp(a, b / 2) % mod;
  if (b % 2 == 0)
    return (k * k) % mod;
  else
    return (((k * k) % mod) * a) % mod;
}
long long a, b, n, first;
int main() {
  cin >> a >> b >> n >> first;
  if (a == 1) {
    n = n % mod;
    n = (n * b) % mod;
    n = n + first;
    n = n % mod;
    cout << n;
  } else {
    long long t = lgp(a, n) % mod, k = 0;
    k = k + (t * first) % mod;
    t--;
    t = (t * lgp(a - 1, mod - 2)) % mod;
    t = (t * b) % mod;
    k = (k + t) % mod;
    cout << k;
  }
  return 0;
}
