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 power(long long x, long long y, long long p) {
  long long res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
long long modInverse(long long n, long long p) { return power(n, p - 2, p); }
int main() {
  long long a, b, n, x, ans, temp, power_n, mod = 1e9 + 7;
  cin >> a >> b >> n >> x;
  if (a == 1) {
    cout << (x + (b * (n % mod))) % mod << endl;
  } else {
    power_n = power(a, n, mod);
    ans = (x * power_n) % mod;
    temp = (power_n - 1) % mod;
    temp = (temp * modInverse(a - 1, mod)) % mod;
    temp = (temp * b) % mod;
    cout << (ans + temp) % mod << endl;
  }
}
