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K Increasing Subsequence 1

For the given sequence A with n different elements find the number of increasing subsequences with k elements.

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K Increasing Subsequence 1

medium

For the given sequence A with n different elements find the number of increasing subsequences with k elements.

Constraints

1. 1 <= n <= 10^5 2. 1 <= k <= 11 3. 1 <= A[i] <= n 4. Output may not fit in 32 bit signed integer

Format

Input

First line contains one integer n Second line contains one integer k following n lines contains elements of sequence A[1] A[2] ....A[n]

Output

Print one number the andwer to question

Example

Sample Input

5 3 1 2 3 5 4

Sample Output

7

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