2008/2009 ACM International Collegiate Programming Contest
University of Ulm Local Contest

# Problem E: El Dorado

Source file: eldorado.(c|cc|hs|java|pas)
Input file: eldorado.in

Bruce Force has gone to Las Vegas, the El Dorado for gamblers. He is interested especially in one betting game, where a machine forms a sequence of n numbers by drawing random numbers. Each player should estimate beforehand, how many increasing subsequences of length k will exist in the sequence of numbers.

A subsequence of a sequence a1, ..., an is defined as ai1, ..., ail, where 1 ≤ i1 < i2 < ... < il ≤ n. The subsequence is increasing, if aij-1 < aij for all 1 < j ≤ l.

Bruce doesn't trust the Casino to count the number of increasing subsequences of length k correctly. He has asked you if you can solve this problem for him.

#### Input Specification

The input contains several test cases. The first line of each test case contains two numbers n and k (1 ≤ k ≤ n ≤ 100), where n is the length of the sequence drawn by the machine, and k is the desired length of the increasing subsequences. The following line contains n pairwise distinct integers ai (-10000 ≤ ai ≤ 10000 ), where ai is the ith number in the sequence drawn by the machine.

The last test case is followed by a line containing two zeros.

#### Output Specification

For each test case, print one line with the number of increasing subsequences of length k that the input sequence contains. You may assume that the inputs are chosen in such a way that this number fits into a 64 bit signed integer (in C/C++, you may use the data type "long long", in Java the data type "long").

#### Sample Input

    10 5
    1 2 3 4 5 6 7 8 9 10
    3 2
    3 2 1
    0 0

#### Sample Output

    252
    0