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. 
n,t = map(int, raw_input().split())
a = map(int, raw_input().split())
#print n,t,a
m = min(t,n)
b = a*m
c = []
c += [a[0]]
for i in b[1:]:
    if i>=c[-1]:
	c += [i]
    else:
	j = len(c) - 2
	while j>=0:
	    if c[j]<=i:
		break
	    j-=1
	c[j+1] = i
    #print c
l = len(c)
#print l
ans = l
if t>m:
    d = {}
    mx = 0
    for i in a:
	if(i in d):
	    d[i]+=1
	else:
	    d[i]=1
	mx = max(mx, d[i])
    #print ans, mx
    ans += (t-m)*mx
print ans
