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;
long long int p(long long int bas, long long int exp) {
  if (exp == 0) return 1LL;
  long long int t = p(bas, exp >> 1LL);
  t = (t * t) % MOD;
  if (exp & 1LL) t = (t * bas) % MOD;
  return t;
}
int main() {
  ios_base::sync_with_stdio(false);
  long long int A, B, n, x;
  cin >> A >> B >> n >> x;
  long long int ans = (p(A, n) * x) % MOD;
  if (A == 1) {
    long long int tmp = n % MOD;
    ans = (ans + B * tmp) % MOD;
  } else {
    long long int tmp = (p(A, n) - 1 + MOD) % MOD;
    tmp = (tmp * B) % MOD;
    ans = (ans + tmp * p((A - 1 + MOD) % MOD, MOD - 2)) % MOD;
  }
  cout << ans << endl;
  return 0;
}
