## Tickets

### Introduce

As a big fan of Formula One, Charlie is really happy with the fact that he has to organize ticket sells for the next Grand Prix race in his own city. Unfortunately, the finacial crisis is striking everywhere and all the banknotes left in his country are valued either $$10$$ euros or $$20$$ euros. The price of all tickets for the race is $$10$$ euros, so whenever someone comes to the ticket store only with $$20$$ euro banknote Charlie must have a $$10$$ euro banknote to give them change. Charlie realize that with the huge deficit of banknotes this could be a problem. Charlie has some priceless information but couldn't make use of it, so he needs your help. Exactly $$n+m$$ people will come to buy a ticket. $$n$$ of them will have only a single $$10$$ euro banknote, and $$m$$ of them will have only a single $$20$$ euro banknote. Currently Charlie has k $$10$$ euro banknotes, which he can use for change if needed. All $$n+m$$ people will come to the ticket store in random order, all orders are equiprobable. Return the probability that the ticket selling process will run smoothly, i.e. Charlie will have change for every person with $$20$$ euro banknote.

### Input

The input consist of a single line with three space separated integers, $$n$$,$$m$$ and $$k$$ $$(0 \le n,m \le 10^5,0 \le k \le 10)$$.

### Output

Output on a single line the desired probability with at least $$4$$ digits after the decimal point.

### Examples

#### Input

5 3 1


#### Output

0.857143


#### Input

0 5 5


#### Output

1


#### Input

0 1 0


#### Output

0


## 题解

• 客户用$$10$$元来买，就是增加一张你手上的$$10$$元。
• 用户用$$20$$元来买，就是减少一张你手上的$$10$$元。

#include<bits/stdc++.h>
using namespace std;
int n,m,k;
double ans;
int main(){
scanf("%d%d%d",&n,&m,&k);
if(n+k<m){printf("0");return 0;}
if(k>=m){printf("1");return 0;}
double ans=1;
for(int j=1;j<=k+1;j++)
ans=ans*(m-k-1+j)/(n+j);
printf("%.4lf",1-ans);
return 0;
}