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=400
R=lambda:map(int,raw_input().split())
n,t=R()
a=R()
def mk(s):
  v=[0]*N
  t=[0]*N
  for x in s:
    c=0
    i=x
    while i>0:
      c=max(c,v[i])
      i-=i&-i
    t[x]=max(t[x],c+1)
    i=x
    while i<N:
      v[i]=max(v[i],c+1)
      i+=i&-i
  return t
if t>n*2:
  f=mk(a*n)
  b=mk([321-x for x in (a*n)[::-1]])
  z=0
  for x in a:
    z=max(z,f[x]+b[321-x]+a.count(x)*(t-2*n))
  print z
else:
  print max(mk(a*t))