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Given a sequence of N (1 ≤ N ≤ 10,000) integers S1, ..., SN (0 ≤ Si < 1,000,000,000), compute the number of distinct increasing subsequences of S with length K (1 ≤ K ≤ 50 and K ≤ N). Input The first line contains the two integers N and K. The following N lines contain the integers of the sequence in order. Output Print a single integer representing the number of distinct increasing subsequences of S of length K, modulo 5,000,000. Example Input: 4 3 1 2 2 10 Output: 1 The only increasing subsequence of length 3 is 1, 2, 10

Given a sequence of N (1 ≤ N ≤ 10,000) integers S1, ..., SN (0 ≤ Si < 1,000,000,000), compute the number of distinct increasing subsequences of S with length K (1 ≤ K ≤ 50 and K ≤ N).

Input

The first line contains the two integers N and K. The following N lines contain the integers of the sequence in order.

Output

Print a single integer representing the number of distinct increasing subsequences of S of length K, modulo 15,111,992.

Example

Input:

4 3

1

2

2

10

Output:

1

The only increasing subsequence of length 3 is 1, 2, 10.

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• Người up: dat1511
• Nguồn bài: Neal Wu