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 $8·10^{18}$.

Input

First line contain two integer values $*n*$ and $*k*$ $(1 ≤ *n* ≤ 10^{5}, 0 ≤ *k* ≤ 10)$ — 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.