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;
long long po(long long a, long long b) {
  long long t = 1;
  a = a % 1000000007;
  while (b) {
    if (b & 1) {
      t = (t * a) % 1000000007;
    }
    b >>= 1;
    a = (a * a) % 1000000007;
  }
  return t;
}
int main() {
  long long a, b, n, x, i, j, k, l;
  scanf("%I64d%I64d%I64d%I64d", &a, &b, &n, &x);
  if (a == 1) {
    n = n % 1000000007;
    printf("%I64d", (x + ((n * b) % 1000000007)) % 1000000007);
    return 0;
  }
  i = (po(a, n) * x) % 1000000007;
  j = po(a - 1, 1000000005);
  k = (((b * (po(a, n) - 1)) % 1000000007) * j) % 1000000007;
  printf("%I64d", (i + k) % 1000000007);
  return 0;
}
