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 bisect import bisect_left

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

indexes = {}
for i, a in enumerate(A):
    if not a in indexes.keys():
        indexes[a] = [i]
    else:
        indexes[a].append(i)

L = [N]
ind = N
while True:
    ind = (ind+1)%(N+1)
    if ind == N: break
    a = A[ind]
    if indexes[a][-1] == ind:
        ind = indexes[a][0]
        L.append(ind)
    else:
        loc = bisect_left(indexes[a], ind)
        ind = indexes[a][loc+1]
    

start_ind = L[(K-1)%len(L)] + 1
if start_ind == N+1: start_ind = 0
in_list = {}
for a in A:
    in_list[a] = 0
ans = []
for i in range(start_ind, N):
    a = A[i]
    if in_list[a] == 0:
        ans.append(a)
        in_list[a] = 1
    else:
        while True:
            b = ans.pop()
            in_list[b] -= 1
            if a == b:
                break

for a in ans:
    print(a, end=' ')
print()
