#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll mod = 1e9+7;
int main() {
    ll a, b, x;
    cin >> a >> b >> x;
    ll ans = x;
    ll num = (x - a) / (a - b);
    num = max(num, 0ll);
    num = num % mod;
    ans += num * (b % mod);
    ans %= mod;
    //cout << ans <<" " <<  num << endl;
    x -= num * (a - b);
    if(x >= a) ans += b;
    ans %= mod;
    cout << ans << endl;
    return 0;
}

### Prompt

Please create a solution in cpp 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<bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll mod = 1e9+7;
int main() {
    ll a, b, x;
    cin >> a >> b >> x;
    ll ans = x;
    ll num = (x - a) / (a - b);
    num = max(num, 0ll);
    num = num % mod;
    ans += num * (b % mod);
    ans %= mod;
    //cout << ans <<" " <<  num << endl;
    x -= num * (a - b);
    if(x >= a) ans += b;
    ans %= mod;
    cout << ans << endl;
    return 0;
}

```