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: $*n*$, $*T*$ ($1 ≤ *n* ≤ 100$, $1 ≤ *T* ≤ 10^{7}$). 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.

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.