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>
const int MAX_N = (int)5e5 + 123;
const double eps = 1e-6;
const int mod = (int)1e9 + 7;
using namespace std;
int binpow(int a, long long int b) {
  int res = 1;
  while (b) {
    if (b & 1) res = 1ll * res * a % mod;
    a = 1ll * a * a % mod;
    b >>= 1;
  }
  return res;
}
int calc(int a, long long int n) {
  if (!n) return 0;
  if (a == 1) return n % mod;
  int q = binpow(a, n) - 1;
  if (q < 0) q += mod;
  return q * 1ll * binpow(a - 1, mod - 2) % mod;
}
int main() {
  long long int n;
  int a, b, x;
  cin >> a >> b >> n >> x;
  int ans = binpow(a, n) * 1ll * x % mod;
  ans = (ans + 1ll * b * calc(a, n) % mod) % mod;
  cout << ans;
  return 0;
}
