#include<bits/stdc++.h>
typedef long long int ll;
typedef unsigned long long int ull;
#define BIG_NUM 2000000000
#define HUGE_NUM 99999999999999999
#define MOD 1000000007
#define EPS 0.000000001
using namespace std;


ll a,b,x;

int main(){

	scanf("%lld %lld %lld",&a,&b,&x);

	ll ans = x%MOD;
	ll mult = max(0LL,(x-b)/(a-b));
	b %= MOD;
	mult %= MOD;

	printf("%lld\n",(ans+b*mult)%MOD);

	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>
typedef long long int ll;
typedef unsigned long long int ull;
#define BIG_NUM 2000000000
#define HUGE_NUM 99999999999999999
#define MOD 1000000007
#define EPS 0.000000001
using namespace std;


ll a,b,x;

int main(){

	scanf("%lld %lld %lld",&a,&b,&x);

	ll ans = x%MOD;
	ll mult = max(0LL,(x-b)/(a-b));
	b %= MOD;
	mult %= MOD;

	printf("%lld\n",(ans+b*mult)%MOD);

	return 0;
}


```