Algorithm

C. The World is a Theatre
time limit per test
2 seconds
memory limit per test
256 megabytes
Problem Link- https://codeforces.com/problemset/problem/131/C
input
standard input
output
standard output

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
Copy
5 2 5
output
Copy
10
input
Copy
4 3 5
output
Copy
3



 

Code Examples

#1 Code Example with C++ Programming

Code - C++ Programming

#include <cstdio>


unsigned long long choose(int x, int y){
    if(y == 0){return 1;}
    return x * choose(x - 1,y - 1) / y;
}


int main(){

    int n(0), m(0), t(0); scanf("%d %d %d", &n, &m, &t);
    unsigned long long result(0);
    for(int k = 4; k < t; k++){result += choose(n,k) * choose(m, t - k);}
    printf("%llu\n", result);
    return 0;
}
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Input

x
–
+
cmd
5 2 5

Output

x
–
+
cmd
10
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Demonstration

Codeforces Solution-C. The World is a Theatre-Solution in C, C++, Java, Python

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