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;
const int mxN = 1e5;
long long _pow(long long a, long long b) {
  long long res = 1;
  while (b) {
    if (b & 1) res = (res * a) % MOD;
    a *= a;
    a %= MOD;
    b >>= 1;
  }
  return res;
}
long long inv(const long long &a) { return _pow(a, MOD - 2) % MOD; }
int main() {
  long long A, B, n, x;
  cin >> A >> B >> n >> x;
  x %= MOD;
  A %= MOD;
  B %= MOD;
  long long sum = (_pow(A, n) * x) % MOD;
  long long sum2;
  if (A == 1)
    sum2 = ((n % MOD) * B) % MOD;
  else
    sum2 = B * (((_pow(A, n) - 1) % MOD * inv(A - 1)) % MOD);
  cout << (sum + sum2 % MOD) % MOD << endl;
}
