A race timing system records n checkpoint values in course order. Count the number of ways to choose exactly k positions p_1 < p_2 < ... < p_k such that the chosen values are strictly increasing (value[p_1] < value[p_2] < ... < value[p_k]). That is, count the strictly increasing subsequences of length exactly k. Two choices differ if they use different sets of positions, even when the values match.

Input format

Line 1: two integers n and k. Line 2: n space-separated integers, the checkpoint values in course order.

Output format

A single integer: the number of strictly increasing length-k subsequences.

Constraints

• 1 <= n <= 60
• 1 <= k <= n + 1
• -1000000000 <= value <= 1000000000
• The answer fits in a signed 64-bit integer.

4 2
1 2 3 4

6

5 3
1 3 2 3 4

5