C. Subsequences
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

For the given sequence with n different elements find the number of increasing subsequences with k + 1 elements. It is guaranteed that the answer is not greater than 8·1018.

Input

First line contain two integer values n and k (1 ≤ n ≤ 105, 0 ≤ k ≤ 10) — the length of sequence and the number of elements in increasing subsequences.

Next n lines contains one integer a i (1 ≤ a i ≤ n) each — elements of sequence. All values a i are different.

Output

Print one integer — the answer to the problem.

Examples
Input
5 212354
Output
7