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;
int a, b, x;
long long n;
long long mod_pow(long long x, long long m) {
  long long res = 1;
  while (m > 0) {
    if (m & 1) res = res * x % mod;
    x = x * x % mod;
    m >>= 1;
  }
  return res;
}
int main() {
  scanf("%d%d%I64d%d", &a, &b, &n, &x);
  long long rev = mod_pow(a - 1, mod - 2);
  long long t = mod_pow(a, n);
  if (a == 1) {
    printf("%I64d\n", (x + (n % mod) * b) % mod);
    return 0;
  }
  long long ans = (t * x % mod + (t - 1) * rev % mod * b % mod) % mod;
  printf("%I64d\n", ans);
  return 0;
}
