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. 
f = lambda: map(int, input().split())
n, m = f()
t = list(f())
d = {i: j for j, i in enumerate(sorted(set(t)))}
t = [d[i] for i in t]
k = len(d)
a = [0] * k
if m < 2 * k:
    for j in t * m:
        a[j] += 1
        q = a[j]
        j += 1
        while j < k and a[j] < q:
            a[j] += 1
            j += 1
    print(a[-1])
    exit()
a = [0] * k
for j in t * k:
    a[j] += 1
    q = a[j]
    j += 1
    while j < k and a[j] < q:
        a[j] += 1
        j += 1
b = [0] * k
t.reverse()
for j in t * k:
    b[j] += 1
    q = b[j]
    j -= 1
    while j > -1 and b[j] < q:
        b[j] += 1
        j -= 1
print(max(a[j] + (m - 2 * k) * t.count(j) + b[j] for j in range(k)))