URI Online Judge | 1645
# El Dorado

Timelimit: 1

Local Contest, University of Ulm Germany

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 a_{1}, ..., a_{n} is defined as a_{i1}, ..., a_{il}, where 1 ≤ i_{1} < i_{2} < ... < 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 ≤

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

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 | Sample Output |

10 5 |
252 0 |