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 N = 100000 + 10;
const int M = 1000000007;
const double PI = atan(1) * 4;
const int oo = 1000000000;
long long A, B, n, x;
long long pw(long long x, long long p) {
  if (!p) return 1;
  long long d = pw(x, p / 2);
  d = (d * d) % M;
  if (p % 2) d = (d * x) % M;
  assert(x <= M);
  assert(d <= M);
  return d;
}
int main() {
  cin >> A >> B >> n >> x;
  if (A == 1) return cout << (n % M * B % M + x) % M, 0;
  long long one = x * pw(A, n) % M;
  long long dom = pw(A, n) - 1;
  long long den = pw(A - 1, M - 2);
  cout << (one + B * ((dom * den) % M) % M) % M << endl;
}
