B. Once Again...
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given an array of positive integers a 1, a 2, ..., 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 a 1, a 2, ..., a n (1 ≤ a i ≤ 300).

Output

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

Examples
Input
4 33 1 4 2
Output
5
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.