We have a sequence of N \times K integers: X=(X_0,X_1,\cdots,X_{N \times K-1}). Its elements are represented by another sequence of N integers: A=(A_0,A_1,\cdots,A_{N-1}). For each pair i, j (0 \leq i \leq K-1,\ 0 \leq j \leq N-1), X_{i \times N + j}=A_j holds.

Snuke has an integer sequence s, which is initially empty. For each i=0,1,2,\cdots,N \times K-1, in this order, he will perform the following operation:

* If s does not contain X_i: add X_i to the end of s.
* If s does contain X_i: repeatedly delete the element at the end of s until s no longer contains X_i. Note that, in this case, we do not add X_i to the end of s.



Find the elements of s after Snuke finished the operations.

Constraints

* 1 \leq N \leq 2 \times 10^5
* 1 \leq K \leq 10^{12}
* 1 \leq A_i \leq 2 \times 10^5
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N K
A_0 A_1 \cdots A_{N-1}


Output

Print the elements of s after Snuke finished the operations, in order from beginning to end, with spaces in between.

Examples

Input

3 2
1 2 3


Output

2 3


Input

5 10
1 2 3 2 3


Output

3


Input

6 1000000000000
1 1 2 2 3 3


Output




Input

11 97
3 1 4 1 5 9 2 6 5 3 5


Output

9 2 6
from sys import exit, setrecursionlimit, stdin, stderr
from functools import reduce
from itertools import *
from collections import *
from bisect import *
from heapq import *
import operator
import math
from fractions import gcd
from random import randint

setrecursionlimit(10**8)

def input():
  return stdin.readline().strip()

def read():
  return int(input())
 
def reads():
  return [int(x) for x in input().split()]

N, K = reads()
A = reads()

skip = [-1] * (N + 1)
first_occ = {}
for i in range(N-1, -1, -1):
  a = A[i]
  if a in first_occ:
    if first_occ[a] < N-1:
      skip[i] = skip[first_occ[a] + 1]
    else:
      skip[i] = first_occ[a] + 1
  else:
    skip[i] = i
  first_occ[a] = i
skip[N] = N

back = [first_occ[A[i]] + 1 for i in range(N)] + [0]
next_state = [skip[back[q]] for q in range(N+1)]


q = skip[0]

rev = {}
memo = {}
i = 0
while True:
  if q in rev:
    j = rev[q]
    break
  rev[q] = i
  memo[i] = q
  q = next_state[q]
  i += 1

m = i - j
q = memo[j + (K - 1 - j) % m]

s = []
while q < N:
  if skip[q] == q:
    s.append(A[q])
    q += 1
  else:
    q = skip[q]

print(*s)