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Competitions

# Equal Sum Sets

Let us consider sets of positive integers less than or equal to n. Note that all elements of a set are different. Also note that the order of elements doesn't matter, that is, both {3, 5, 9} and {5, 9, 3} mean the same set.

Specifying the number of set elements and their sum to be k and s, respectively, sets satisfying the conditions are limited. When n = 9, k = 3 and s = 23, {6, 8, 9} is the only such set. There may be more than one such set, in general, however. When n = 9, k = 3 and s = 22, both {5, 8, 9} and {6, 7, 9} are possible.

You have to write a program that calculates the number of the sets that satisfy the given conditions.

#### Input

Consists of multiple datasets. The number of datasets does not exceed 100.

Each of the datasets has three integers n, k and s (1n20, 1k10 and 1s155) in one line, separated by a space.

The end of the input is indicated by a line containing three zeros.

#### Output

The output for each dataset should be a line containing a single integer that gives the number of the sets that satisfy the conditions. No other characters should appear in the output.

You can assume that the number of sets does not exceed 2311.

Time limit 1 seconds
Memory limit 128 MiB
Input example #1
9 3 23
9 3 22
10 3 28
16 10 107
20 8 102
20 10 105
20 10 155
3 4 3
4 2 11
0 0 0

Output example #1
1
2
0
20
1542
5448
1
0
0

Source 2013 ACM International Collegiate Programming Contest, Asia Regional Contest, Aizu, November 24, Problem A