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
# -*- coding: utf-8 -*-
"""
Created on Sun Jul 21 23:25:47 2019

@author: Yamazaki Kenichi
"""
import bisect

N, K = map(int,input().split())
A = list(map(int,input().split()))

T = [[] for _ in range(2*10**5+1)]

for i in range(N):
    T[A[i]].append(i)

s = A[0]
pointa = 0
counta, res = 0, [-1]
while True:
    tmp = bisect.bisect_right(T[s], pointa) % len(T[s])
    p_pointa = pointa
    pointa = T[s][tmp] + 1
    if pointa == p_pointa + 1 or pointa < p_pointa:
        counta += 1
        res.append(p_pointa)
    if pointa == N:
        counta += 1
        res.append(p_pointa)
        break
    s = A[pointa]

ans = []
if K % counta != 0:
    pointa = res[K % counta]
#    ans.append(A[pointa])
    while pointa < N:
        if pointa < T[A[pointa]][-1]:
            tmp = bisect.bisect_right(T[A[pointa]],pointa)
            pointa = T[A[pointa]][tmp] + 1
        else:
            ans.append(A[pointa])
            pointa += 1
#        print(ans)
print(' '.join(map(str,ans)))
