#include <iostream>
using namespace std;
int main(void){
    long long a, b, x;
    cin >> a >> b >> x;
    long long c = max(0ll, x - b) / (a - b);  //0もlong long型であるからllをつける
    x %= 1000000007;
    c %= 1000000007;
    b %= 1000000007;
    cout << (b * c + x) % 1000000007 << endl;
}


### 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>
using namespace std;
int main(void){
    long long a, b, x;
    cin >> a >> b >> x;
    long long c = max(0ll, x - b) / (a - b);  //0もlong long型であるからllをつける
    x %= 1000000007;
    c %= 1000000007;
    b %= 1000000007;
    cout << (b * c + x) % 1000000007 << endl;
}


```