A8311 | 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.

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

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.