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;
int mod = 1000000007;
long long pow(long long a, long long b, int MOD) {
  long long x = 1, y = a;
  while (b > 0) {
    if (b % 2 == 1) {
      x = (x * y);
      if (x > MOD) x %= MOD;
    }
    y = (y * y);
    if (y > MOD) y %= MOD;
    b /= 2;
  }
  return x;
}
int main() {
  long long a, b, n, x;
  cin >> a >> b >> n >> x;
  if (a == 1) {
    long long ans = (n % mod * b) % mod;
    ans = (ans + x) % mod;
    cout << ans;
    return 0;
  }
  long long an = pow(a, n, mod), inv = pow(a - 1, mod - 2, mod);
  long long ans = (an * x) % mod, temp;
  temp = (b * inv) % mod;
  temp *= ((an - 1) % mod + mod) % mod;
  temp %= mod;
  ans += temp;
  ans %= mod;
  cout << ans;
}
