1736: El Dorado

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, ..., a_n is defined a_s a_i1, ..., a_il, where 1 ≤ i₁ < i₂ < ... < i_l ≤ n. The subsequence is increasing, if a_ij-1 < a_ij 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.

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 a_i (-10000 ≤ a_i ≤ 10000 ), where ai is the i-th number in the sequence drawn by the machine.

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").

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

252
0