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.
The only line of the input data contains three integers n, m, t (4 ≤ n ≤ 30, 1 ≤ m ≤ 30, 5 ≤ t ≤ n + m).
OutputFind 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.
Examples5 2 5
10
4 3 5
3
c[i][j]=c[i-1][j]+c[i-1][j-1]:即第j个数在前i-1个数选与不选的情况(注意i>=j)
#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<map>
#include<vector>
#include<queue>
#include<algorithm>
#include<stack>
#include<cstdlib>
#include<cctype>
using namespace std;
#define ll long long
typedef pair<ll,int>P;
const int len=1e2+5;
ll c[31][31];
int main()
{
for(int i=0;i<=30;++i)c[i][0]=1;
for(int i=0;i<=30;++i)c[i][i]=1;
for(int i=1;i<=30;++i)
for(int j=1;j<=i;++j)c[i][j]=c[i-1][j]+c[i-1][j-1];
ll a,b,t;
while(cin>>a>>b>>t)
{
ll ans=0;
for(int i=4;i<t;++i)
if(i<=a&&t-i<=b)
ans+=c[a][i]*c[b][t-i];
cout<<ans<<endl;
}
}