#include "bits/stdc++.h"
using namespace std;
#define int long long
#define endl '\n'
int mod=1e9+7;
int mod2=998244353;
const int INF=1e9;

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

### Prompt

Please formulate 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 "bits/stdc++.h"
using namespace std;
#define int long long
#define endl '\n'
int mod=1e9+7;
int mod2=998244353;
const int INF=1e9;

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

```