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>
using namespace std;
const int mod = 1e9 + 7;
long long mul(long long a, long long b) {
  long long ans = 1;
  a = a % mod;
  while (b > 0) {
    if (b % 2 == 1) ans = ans * a % mod;
    b = b / 2;
    a = a * a % mod;
  }
  return ans;
}
int main() {
  long long A, B, x, n;
  while (~scanf("%lld %lld %lld %lld", &A, &B, &n, &x)) {
    long long ans, t, An;
    if (A == 1) {
      ans = (x + n % mod * B) % mod;
      printf("%d\n", (int)ans);
    } else {
      An = mul(A, n);
      t = mul(A - 1, mod - 2);
      ans = (((An - 1) * t % mod) * B % mod + An * x % mod) % mod;
      printf("%d\n", (int)ans);
    }
  }
  return 0;
}
