#include <bits/stdc++.h>
using namespace std;
template <class T>
T mulmod(T a, T b) {
  if (b == 0) return 0;
  if (b == 1) return a;
  T x = mulmod(a, b >> 1);
  x = (x + x) % 1000000007;
  if (b & 1) x = (x + a) % 1000000007;
  return x;
}
template <class T>
T larger(T a, T b) {
  return (a > b ? a : b);
}
template <class T>
T smaller(T a, T b) {
  return (a < b ? a : b);
}
template <class T>
T gcd(T a, T b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
template <class T>
T lcm(T a, T b) {
  return (a * b) / gcd(a, b);
}
template <class T>
string converter(T n) {
  stringstream x;
  x << n;
  return x.str();
}
template <class T>
T pw(T a, T b) {
  if (b == 0) return 1;
  T x = pw(a, b >> 1);
  x = mulmod(x, x);
  if (b & 1) x = mulmod(x, a);
  return x;
}
template <class T1>
void deb(T1 e1) {
  cout << e1 << endl;
}
template <class T1, class T2>
void deb(T1 e1, T2 e2) {
  cout << e1 << " " << e2 << endl;
}
template <class T1, class T2, class T3>
void deb(T1 e1, T2 e2, T3 e3) {
  cout << e1 << " " << e2 << " " << e3 << endl;
}
template <class T1, class T2, class T3, class T4>
void deb(T1 e1, T2 e2, T3 e3, T4 e4) {
  cout << e1 << " " << e2 << " " << e3 << " " << e4 << endl;
}
template <class T1, class T2, class T3, class T4, class T5>
void deb(T1 e1, T2 e2, T3 e3, T4 e4, T5 e5) {
  cout << e1 << " " << e2 << " " << e3 << " " << e4 << " " << e5 << endl;
}
template <class T1, class T2, class T3, class T4, class T5, class T6>
void deb(T1 e1, T2 e2, T3 e3, T4 e4, T5 e5, T6 e6) {
  cout << e1 << " " << e2 << " " << e3 << " " << e4 << " " << e5 << " " << e6
       << endl;
}
void letsgo() {
  long long int a, b, x, n;
  cin >> a >> b >> n >> x;
  if (a == 1) {
    cout << (x + (n % 1000000007 * b) % 1000000007) % 1000000007;
    return;
  }
  long long int aN = pw(a, n);
  long long int ans = (aN * x) % 1000000007;
  long long int z = ((aN - 1 + 1000000007) % 1000000007 * b) % 1000000007;
  z = (z * pw(a - 1, 1000000007 - 2ll)) % 1000000007;
  cout << (ans + z) % 1000000007;
}
int main() {
  letsgo();
  return 0;
}

### Prompt

In CPP, your task is to solve the following problem:

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;
template <class T>
T mulmod(T a, T b) {
  if (b == 0) return 0;
  if (b == 1) return a;
  T x = mulmod(a, b >> 1);
  x = (x + x) % 1000000007;
  if (b & 1) x = (x + a) % 1000000007;
  return x;
}
template <class T>
T larger(T a, T b) {
  return (a > b ? a : b);
}
template <class T>
T smaller(T a, T b) {
  return (a < b ? a : b);
}
template <class T>
T gcd(T a, T b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
template <class T>
T lcm(T a, T b) {
  return (a * b) / gcd(a, b);
}
template <class T>
string converter(T n) {
  stringstream x;
  x << n;
  return x.str();
}
template <class T>
T pw(T a, T b) {
  if (b == 0) return 1;
  T x = pw(a, b >> 1);
  x = mulmod(x, x);
  if (b & 1) x = mulmod(x, a);
  return x;
}
template <class T1>
void deb(T1 e1) {
  cout << e1 << endl;
}
template <class T1, class T2>
void deb(T1 e1, T2 e2) {
  cout << e1 << " " << e2 << endl;
}
template <class T1, class T2, class T3>
void deb(T1 e1, T2 e2, T3 e3) {
  cout << e1 << " " << e2 << " " << e3 << endl;
}
template <class T1, class T2, class T3, class T4>
void deb(T1 e1, T2 e2, T3 e3, T4 e4) {
  cout << e1 << " " << e2 << " " << e3 << " " << e4 << endl;
}
template <class T1, class T2, class T3, class T4, class T5>
void deb(T1 e1, T2 e2, T3 e3, T4 e4, T5 e5) {
  cout << e1 << " " << e2 << " " << e3 << " " << e4 << " " << e5 << endl;
}
template <class T1, class T2, class T3, class T4, class T5, class T6>
void deb(T1 e1, T2 e2, T3 e3, T4 e4, T5 e5, T6 e6) {
  cout << e1 << " " << e2 << " " << e3 << " " << e4 << " " << e5 << " " << e6
       << endl;
}
void letsgo() {
  long long int a, b, x, n;
  cin >> a >> b >> n >> x;
  if (a == 1) {
    cout << (x + (n % 1000000007 * b) % 1000000007) % 1000000007;
    return;
  }
  long long int aN = pw(a, n);
  long long int ans = (aN * x) % 1000000007;
  long long int z = ((aN - 1 + 1000000007) % 1000000007 * b) % 1000000007;
  z = (z * pw(a - 1, 1000000007 - 2ll)) % 1000000007;
  cout << (ans + z) % 1000000007;
}
int main() {
  letsgo();
  return 0;
}

```