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
# Your code here!

import sys
sys.setrecursionlimit(10**6)
readline = sys.stdin.readline #文字列入力のときは注意

n,k = [int(i) for i in readline().split()]
a = [int(i) for i in readline().split()]

memo = dict()
res = [0]*(2*n)
for i,c in enumerate(a*2):
    if c in memo: res[memo[c]] = i+1
    memo[c] = i

#print(res)

res2 = res[:n]

for i in range(n-1,-1,-1):
    if res2[i] < n:
        res2[i] = res2[res2[i]]

cycle = [0]
offset = 0
now = res2[0]-n

while now != 0:
    if now == n:
        offset = 1
        break
    else:
        cycle.append(now)
        now = res2[now]-n

#print(res2)
#print(cycle,offset)

l = len(cycle)
k-=1
k %= (l+offset)

#print("k =",k)

if k != l: ans = cycle[k]
else: exit()
while res[ans] < n:
    ans = res[ans]

"""
if k != l: ans = p = cycle[k]
else: ans = p = n+1
while p <= n:
    ans = p
    p = res[p]
#    print(ans,p)
"""


if ans >= n: exit()
else:
    s = []
    ss = set()
    for i in range(ans,n):
        if a[i] in ss:
            while a[i] in ss:
                c = s.pop()
                ss.remove(c)
        else:
            s.append(a[i])
            ss.add(a[i])
    
print(" ".join(map(str,s)))


