#include <bits/stdc++.h>
using namespace std;
const long long MOD = 1e9 + 7;
long long inv(long long x) {
  long long c = MOD - 2;
  long long ans = 1;
  while (c) {
    if (c & 1) ans = ans * x % MOD;
    c >>= 1;
    x = x * x % MOD;
  }
  return ans;
}
long long qpow(long long A, long long n) {
  long long ans = 1;
  while (n) {
    if (n & 1) ans = ans * A % MOD;
    n >>= 1;
    A = A * A % MOD;
  }
  return ans;
}
int main() {
  long long A, B, n, x;
  cin >> A >> B >> n >> x;
  if (A == 1)
    cout << (B * (n % MOD) + x) % MOD << endl;
  else
    cout << ((qpow(A, n) + MOD - 1) % MOD * inv(A - 1) % MOD * B % MOD +
             qpow(A, n) * x % MOD) %
                MOD
         << endl;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const long long MOD = 1e9 + 7;
long long inv(long long x) {
  long long c = MOD - 2;
  long long ans = 1;
  while (c) {
    if (c & 1) ans = ans * x % MOD;
    c >>= 1;
    x = x * x % MOD;
  }
  return ans;
}
long long qpow(long long A, long long n) {
  long long ans = 1;
  while (n) {
    if (n & 1) ans = ans * A % MOD;
    n >>= 1;
    A = A * A % MOD;
  }
  return ans;
}
int main() {
  long long A, B, n, x;
  cin >> A >> B >> n >> x;
  if (A == 1)
    cout << (B * (n % MOD) + x) % MOD << endl;
  else
    cout << ((qpow(A, n) + MOD - 1) % MOD * inv(A - 1) % MOD * B % MOD +
             qpow(A, n) * x % MOD) %
                MOD
         << endl;
}

```