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
import sys
input = sys.stdin.readline
from collections import *

N, K = map(int, input().split())
A = list(map(int, input().split()))
log_size = 65
#行き先ではなく移動量をダブリングする
dp = [[-1]*N for _ in range(log_size)]
idx = defaultdict(int)

for i in range(2*N):
    if A[i%N] in idx and idx[A[i%N]]<N:
        dp[0][idx[A[i%N]]] = i+1-idx[A[i%N]]
    
    idx[A[i%N]] = i

for i in range(1, log_size):
    for j in range(N):
        #値が大きくなりすぎるとTLEする
        dp[i][j] = min(10**18, dp[i-1][j]+dp[i-1][(j+dp[i-1][j])%N])

now = 0
NK = N*K

for i in range(log_size-1, -1, -1):
    if NK-dp[i][now]>=0:
        NK -= dp[i][now]
        now = (now+dp[i][now])%N

if NK==0:
    print()
    exit()
    
q = deque([])
cnt = defaultdict(int)

for i in range(now, N):
    if cnt[A[i]]>0:
        while cnt[A[i]]>0:
            rem = q.pop()
            cnt[rem] -= 1
    else:
        cnt[A[i]] += 1
        q.append(A[i])

print(*q)