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 bisect
def LIS(As):
    L = [As[0]]
    for a in As[1:]:
        if a >= L[-1]:
            L.append(a)
        else:
            pos = bisect.bisect_right(L, a)
            L[pos] = a
    return L

def solve():
    n,T = map(int,input().split())
    array = list(map(int,input().split()))
    if (T<=n+1):
        print (len(LIS(array*T)))
    else:
        newarray = array*n
        lis = LIS(newarray)
        newlis = LIS(newarray+array)
        print (len(newlis)+(len(newlis)-len(lis))*(T-n-1))

solve()