E - The World is a Theatre

E - The World is a Theatre

Time Limit:2000MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u

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Description

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.

Sample Input

Input

5 2 5

Output

10

Input

4 3 5

Output

3

小结：

        感觉想法和划分数差不多....大概的想法是，DP[i][j]表示从i中取j个的取法，这里的i，j个物品没有区别。

        然后就有状态转移方程DP[i][j]=DP[i-1][j]+DP[i-1][j-1].

以下是AC代码：

#include<stdio.h>
#include<string.h>
int main()
{
    int n,m,t;
    scanf("%d%d%d",&n,&m,&t);
    long long dp[65][65];
    memset(dp,0,sizeof(dp));
    for(int i=0;i<=30;i++)
    {
        dp[i][0]=1;
        for(int j=1;j<=i;j++)
        {
            dp[i][j]=dp[i-1][j]+dp[i-1][j-1];
        }
    }
    long long ans=0;
    for(int i=4;i<t;i++)
    {
        ans+=dp[n][i]*dp[m][t-i];
    }
    printf("%lld\n",ans);
    return 0;
}