1443: Binomial Showdown

In how many ways can you choose k elements out of n elements, not taking order into account? Write a program to compute this number.

The input will contain one or more test cases. Each test case consists of one line containing two integers n (n>=1) and k (0<=k<=n). Input is terminated by two zeroes for n and k.

For each test case, print one line containing the required number. This number will always fit into an integer, i.e. it will be less than 2³¹. Warning: Don‘t underestimate the problem. The result will fit into an integer - but if all intermediate results arising during the computation will also fit into an integer depends on your algorithm. The test cases will go to the limit.

4 2
10 5
49 6
0 0

6
252
13983816

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