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

n, T = map(int, input().split())
As = list(map(int, input().split()))

def solve(n, T, As):
    if T <= 201:
        return len(LIS(As * T))
    lis = LIS(As * n)
    revAs = [-a for a in As[::-1]]
    lisrev = LIS(revAs * n)
    lisrev.sort()
    freq = [0] * 301
    for a in As:
        freq[a] += 1
    record = 0
    for a, f in enumerate(freq[1:], 1):
        if f == 0:
            continue
        head = bisect.bisect_right(lis, a)
        tail = bisect.bisect_right(lisrev, -a)
        length = head + tail + f * (T - 2*n)
        if length > record:
            record = length
    return record


def LIS(As):
    '''数列As の最長非減少部分列の長さを求める。
    '''
    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

print(solve(n, T, As))