#include <iostream>
#include <algorithm>

using namespace std;

#define MOD 1000000007

int main(){
  long long a, b, x;
  cin >> a >> b >> x;
  long long ret = x % MOD;
  if(x < a){
    cout << x % MOD << endl;
    return 0;
  }
  long long d = b - a;
  long long n = (x - a) / -d + 1;
  long long l = x + (n-1)*d;
  //cout << d << " " << n << " " << l << endl;
  ret = (ret +  ((n % MOD) *(b % MOD) % MOD)) % MOD;
  cout << ret << endl;
  return 0;
}


### Prompt

Your task is to create a CPP solution to the following problem:

Problem

If you bring an empty bottle of $ a $ milk, you can exchange it for a new bottle of $ b $ milk.
How many bottles of milk can Mr. Kawabayashi, who initially has a bottle of $ x $ milk, drink? Output the remainder after dividing by $ 1000000007 $.

Constraints

The input satisfies the following conditions.

* $ 1 \ leq a \ leq 10 ^ {15} $
* $ 0 \ leq b \ lt a $
* $ 0 \ leq x \ leq 10 ^ {15} $

Input

The input is given in the following format.


$ a $ $ b $ $ x $


Three integers $ a $, $ b $, $ x $ are given, separated by spaces.

Output

Print the answer on one line.

Examples

Input

3 1 5


Output

7


Input

3 2 5


Output

11


Input

82 69 64


Output

64


Input

316250877917604 316250877917599 681260158257385


Output

62687552

### Response

```cpp
#include <iostream>
#include <algorithm>

using namespace std;

#define MOD 1000000007

int main(){
  long long a, b, x;
  cin >> a >> b >> x;
  long long ret = x % MOD;
  if(x < a){
    cout << x % MOD << endl;
    return 0;
  }
  long long d = b - a;
  long long n = (x - a) / -d + 1;
  long long l = x + (n-1)*d;
  //cout << d << " " << n << " " << l << endl;
  ret = (ret +  ((n % MOD) *(b % MOD) % MOD)) % MOD;
  cout << ret << endl;
  return 0;
}


```