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
sys.setrecursionlimit(10**6)
from collections import defaultdict

N,K = map(int,input().split())
A = [int(x) for x in input().split()]

AA = A + A # 2周分
next_same = [None] * (2*N)
last_pos = defaultdict(lambda: None)

for i,a in enumerate(AA):
    j = last_pos[a]
    if j is None:
        last_pos[a] = i
    else:
        next_same[j] = i
        last_pos[a] = i

# Xの添字で、最後にvisitしたときを持つ。visit = （そこからスタート！）

NK = N * K
visited = [None] * N
x = 0
visited[0] = 0
while True:
    y = next_same[x % N] + (x//N) * N + 1
    if y >= NK:
        break
    if visited[y % N] is not None:
        # 周期が見つかった！
        P = y - visited[y % N]
        y += (NK - y) // P * P
        x = y
        break
    else:
        visited[y % N] = y
        x = y

answer = []
while x < NK:
    y = next_same[x % N] + (x//N) * N + 1
    if y > NK:
        answer.append(A[x%N])
        x += 1
        continue
    x = y

print(' '.join(map(str,answer)))