#include <bits/stdc++.h>
#define chmin(a, b) ((a)=min((a), (b)))
#define chmax(a, b) ((a)=max((a), (b)))
#define fs first
#define sc second
#define eb emplace_back
using namespace std;

typedef long long ll;
typedef pair<int, int> P;
typedef tuple<int, int, int> T;

const ll MOD=1e9+7;
const ll INF=1e18;
const double pi=acos(-1);
const double eps=1e-10;

int dx[]={1, -1, 0, 0};
int dy[]={0, 0, 1, -1};

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

### Prompt

Construct a CPP code solution to the problem outlined:

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>
#define chmin(a, b) ((a)=min((a), (b)))
#define chmax(a, b) ((a)=max((a), (b)))
#define fs first
#define sc second
#define eb emplace_back
using namespace std;

typedef long long ll;
typedef pair<int, int> P;
typedef tuple<int, int, int> T;

const ll MOD=1e9+7;
const ll INF=1e18;
const double pi=acos(-1);
const double eps=1e-10;

int dx[]={1, -1, 0, 0};
int dy[]={0, 0, 1, -1};

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

```