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 long long mod = 1e9 + 7;
long long power(long long x, long long y) {
  long long ans = 1ll;
  long long ret = x;
  while (y) {
    if (y & 1ll) ans = (ans * ret) % mod;
    ret = (ret * ret) % mod;
    y /= 2ll;
  }
  return ans;
}
int32_t main() {
  long long a, b, n, x;
  cin >> a >> b >> n >> x;
  if (n == 1) return cout << (a * x + b) % mod << endl, 0;
  if (a == 1) return cout << (x + ((n) % mod) * b) % mod << endl, 0;
  long long d =
      (((b * ((power(a, n) - 1ll) + mod)) % mod) * power(a - 1ll, mod - 2ll)) %
      mod;
  long long c = (power(a, n) * x) % mod;
  return cout << (c + d) % mod << endl, 0;
}
