You are given an array of positive integers a₁, a₂, ..., a_n × T of length n × T. We know that for any i > n it is true that a_i = a_i - n. Find the length of the longest non-decreasing sequence of the given array.

Input

The first line contains two space-separated integers: n, T (1 ≤ n ≤ 100, 1 ≤ T ≤ 10⁷). The second line contains n space-separated integers a₁, a₂, ..., a_n (1 ≤ a_i ≤ 300).

Output

Print a single number — the length of a sought sequence.

Note

The array given in the sample looks like that: 3, 1, 4, 2, 3, 1, 4, 2, 3, 1, 4, 2. The elements in bold form the largest non-decreasing subsequence.

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Examples