Problem:
Problem A: 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

The input consists of multiple datasets. The number of datasets does not exceed 100.

Each of the datasets has three integers n, k and s in one line, separated by a space. You may assume 1 ≤ n ≤ 20, 1 ≤ k ≤ 10 and 1 ≤ s ≤ 155.

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 231 - 1.

Sample Input

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 for the Sample Input

1
2
0
20
1542
5448
1
0
0

Solution in C# (judge verdict: Accepted)

using System;
public class AOJ1335
{
	public static void Main ()
	{
		new AOJ1335 ();
	}

	Scanner sc;
	int N, K, S;

	public AOJ1335 ()
	{
		sc = new Scanner (Console.In);
		while (sc.HasNext()) {
			N = sc.NextInt ();	K = sc.NextInt ();	S = sc.NextInt ();
			if (N == 0)	break;
			solve ();
		}
	}
	void solve ()
	{
		Console.WriteLine (f1 (N, S, 1));
	}

	int f1 (int prev, int sum, int depth)
	{
		if (depth > K)	return sum == 0 ? 1 : 0;
		if (sum <= 0)	return 0;

		int ret = 0;
		for (int i=prev; i>=1; --i)	ret += f1 (i - 1, sum - i, depth + 1);
		return ret;
	}
}



public class Scanner
{
	int p, n;
	const int MAX = 1 << 10;
	System.IO.TextReader src;
	char[] buf = new char[MAX];
	bool[] isSpace = new bool[128];

	public Scanner (System.IO.TextReader src)
	{
		this.src = src;
		isSpace [' '] = isSpace ['\n'] = isSpace ['\r'] = isSpace ['\t'] = true;
	}
			
	private int Read ()
	{
		if (n == -1)
			return -1;
		if (p >= n) {
			p = 0;
			n = src.Read (buf, 0, MAX);
			if (n <= 0) {
				n = -1;
				return -1;
			}
		}
		return buf [p++];
	}

	public bool HasNext ()
	{
		int c = Read ();
		while (c>=0 && isSpace[c])
			c = Read ();
		if (c == -1)
			return false;
		--p;
		return true;
	}

	public int NextInt ()
	{
		if (!HasNext ())
			throw new Exception ("NoSuchElementException");
		int c = Read (), sign = 1;
		if (c == '-') {
			sign = -1;
			c = Read ();
		}
		int ret = 0;
		do {
			if (!('0' <= c && c <= '9'))
				throw new Exception ("InputMismatchException " + (char)c);
			ret = ret * 10 + (int)(c - '0');
			c = Read ();
		} while(c>=0 && !isSpace[c]);
		return ret * sign;
	}

}