#include <bits/stdc++.h>
typedef long long ll;
typedef long double ld;
const int INF=1e9,MOD=1e9+7;
const ll LINF=1e18;
using namespace std;
#define int long long

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


### Prompt

In Cpp, your task is to solve 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>
typedef long long ll;
typedef long double ld;
const int INF=1e9,MOD=1e9+7;
const ll LINF=1e18;
using namespace std;
#define int long long

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


```