Codeforces Beta Round #95 (Div. 2) C. The World is a Theatre 组合数学

C. The World is a Theatre

There are n boys and m girls attending a theatre club. To set a play "The Big Bang Theory", they need to choose a group containing exactly t actors containing no less than 4 boys and no less than one girl. How many ways are there to choose a group? Of course, the variants that only differ in the composition of the troupe are considered different.

Perform all calculations in the 64-bit type: long long for С/С++, int64 for Delphi and long for Java.

Input

The only line of the input data contains three integers n, m, t (4 ≤ n ≤ 30, 1 ≤ m ≤ 30, 5 ≤ t ≤ n + m).

Output

Find the required number of ways.

Please do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specificator.

Examples

input

5 2 5

output

10

input

4 3 5

output

3
思路：在4个男生1个女生的基础上暴力求组合数；不好描述见代码；
　　　

#include<iostream>
#include<cstdio>
#include<cmath>
#include<string>
#include<queue>
#include<algorithm>
#include<stack>
#include<cstring>
#include<vector>
#include<list>
#include<set>
#include<map>
using namespace std;
#define ll long long
#define inf 2000000001
int scan()
{
    int res = 0 , ch ;
    while( !( ( ch = getchar() ) >= '0' && ch <= '9' ) )
    {
        if( ch == EOF )  return 1 << 30 ;
    }
    res = ch - '0' ;
    while( ( ch = getchar() ) >= '0' && ch <= '9' )
        res = res * 10 + ( ch - '0' ) ;
    return res ;
}
ll combine1(ll n,ll m) //计算组合数C(n,m)
{
    ll sum=1; //线性计算
    for(ll i=1,j=n;i<=m;i++,j--)
        sum=sum*j/i;
    return sum;
}
int main()
{
    ll x,y,z,i,t;
    scanf("%I64d%I64d%I64d",&x,&y,&z);
    int b=4,g=z-4;
    ll ans=0;
    for(i=4;i<=x;i++)
    {
        b=i;
        g=z-i;
        if(g>y||g<1)continue;
        ans+=combine1(x,b)*combine1(y,g);
    }
    cout<<ans<<endl;
    return 0;
}