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 bisect import bisect_right
import sys
N, K = map(int, input().split())
A = list(map(int, input().split()))
a_to_i = [[] for _ in range(max(A)+1)]
for i in range(N):
    a_to_i[A[i]].append(i)
next_index = [-1]*N
for i in range(N):
    a = A[i]
    j = bisect_right(a_to_i[a], i)
    if j == len(a_to_i[a]):
        next_index[i] = a_to_i[a][0]+N
    else: next_index[i] = a_to_i[a][j]
now = 0
cnt = 0
while True:
    i = next_index[now]
    if i>=N:
        i%=N
        cnt+=1
    else: now = i
    i+=1
    if i>=N:
        cnt+=1
        i%=N
    now = i
    if now == 0:
        break
K%=cnt
if K==0:
    print()
    sys.exit()
ans = [A[0]]
K*=N
K-=1
now = 0
while now<K:
    ni = next_index[now%N]+1
    if(now//N)*N+ni-1 == K:
        ans.pop()
        break
    if (now//N)*N+ni>K:
        now+=1
        ans.append(A[now%N])
    else:
        now = (now//N)*N+ni
        ans[-1] = A[now%N]




print(*ans, sep = ' ')







    
