#include <bits/stdc++.h>

using namespace std;
using ll = long long;
using ull = unsigned long long;
template <class T> using V = vector<T>;
template <class T> using VV = V<V<T>>;

int main() {
	ll a,b,x;
	cin>>a>>b>>x;
	const int mod=1000000007;
	ll ans=x;
	if(x>=a){
		ans+=((x-a)/(a-b)+1)%mod*(b%mod)%mod;
	}
	ans%=mod;
	cout<<ans<<endl;
    return 0;
}


### Prompt

Please provide a cpp coded solution to the problem described below:

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;
using ll = long long;
using ull = unsigned long long;
template <class T> using V = vector<T>;
template <class T> using VV = V<V<T>>;

int main() {
	ll a,b,x;
	cin>>a>>b>>x;
	const int mod=1000000007;
	ll ans=x;
	if(x>=a){
		ans+=((x-a)/(a-b)+1)%mod*(b%mod)%mod;
	}
	ans%=mod;
	cout<<ans<<endl;
    return 0;
}


```