#include <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <bitset>
#include <map>
#include <tuple>
#include <unordered_set>
#include <unordered_map>
#include <list>
#include <numeric>
#include <utility>
#include <iterator>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <cstring>
#include <climits>
#include <ctime>
#include <cassert>
#include <random>
#include <cstring>

#define rep(i,n) for(int i=0;i<int(n);i++)
#define all(x) (x).begin(),x.end()
#define pb push_back

using namespace std;
using ll = long long;

const ll mod = 1000000007;
int dx[4]={1,0,-1,0};
int dy[4]={0,1,0,-1};
int ddx[8]={-1,-1,0,1,1,1,0,-1};
int ddy[8]={0,1,1,1,0,-1,-1,-1};
bool debug=false;

/*---------------------------------------------------*/

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


### Prompt

Develop a solution in Cpp 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 <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <bitset>
#include <map>
#include <tuple>
#include <unordered_set>
#include <unordered_map>
#include <list>
#include <numeric>
#include <utility>
#include <iterator>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <cstring>
#include <climits>
#include <ctime>
#include <cassert>
#include <random>
#include <cstring>

#define rep(i,n) for(int i=0;i<int(n);i++)
#define all(x) (x).begin(),x.end()
#define pb push_back

using namespace std;
using ll = long long;

const ll mod = 1000000007;
int dx[4]={1,0,-1,0};
int dy[4]={0,1,0,-1};
int ddx[8]={-1,-1,0,1,1,1,0,-1};
int ddy[8]={0,1,1,1,0,-1,-1,-1};
bool debug=false;

/*---------------------------------------------------*/

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


```