You are given an array of positive integers a1, a2, ..., an × T of length n × T. We know that for any i > n it is true that ai = ai - 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, ..., an (1 ≤ ai ≤ 300).

Output

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

Examples

Input

4 3
3 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. 
import sys
input = sys.stdin.readline 

n, t = map(int, input().split())
a = list(map(int, input().split()))

dp = [0 for _ in range(301)]

for i in a * min(t, 2 * n): 
  dp[i] = max(dp[:i + 1]) + 1

max_n = max(dp)


count = [0 for _ in range(301)]
for x in a: 
  count[x] += 1

print(max_n + max((t - n * 2) * max(count), 0))