### El Dorado

#### Problem Description

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*, where

_{i1}, ..., a_{il}*1 ≤ i*. The subsequence is increasing, if

_{1}< i_{2}< ... < i_{l}≤ n*a*for all

_{ij-1}< a_{ij}*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

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*), where

_{i}≤ 10000*a*is the

_{i}*i*

^{th}number in the sequence drawn by the machine.

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

#### Output

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