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 collections import deque
N, K = map(int, input().split())
A = list(map(int, input().split()))
next_step = [0] * N
memo = [-1] * (2*10**5)
cnt = 0
for i, a in enumerate(A+A):
    if memo[a-1] >= 0:
        if next_step[memo[a-1]%N]:
            continue
        next_step[memo[a-1]%N] = i - memo[a-1] + 1
        if next_step[memo[a-1]%N] == 0:
            pass
        cnt += 1
    if cnt == N:
        break
    memo[a-1] = i

j = 0
while True:
    if j + next_step[j%N] < N*K:
        j += next_step[j%N]
        if j%N == 0:
            j = max(j, N*K//j*j)
    else:
        break

q = deque()
memo = [-1] * (2*10**5)
cnt = 0
for k in range(j, N*K):
    a = A[k%N]
    if memo[a-1] < 0:
        q.append(a)
        memo[a-1] = cnt
        cnt += 1
    else:
        while True:
            b = q.pop()
            memo[b-1] = -1
            if b == a:
                break

print(*q)
