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

N, K = map(int, input().split())
A = list(map(int, input().split()))
first_idx = {}
for i in range(N)[::-1]:
    first_idx[A[i]] = i
next_idx = {}
dist = [[0] * N for _ in range(41)]
for i in range(N)[::-1]:
    if A[i] in next_idx:
        dist[0][i] = next_idx[A[i]] - i + 1
    else:
        dist[0][i] = N - i + first_idx[A[i]] + 1
    next_idx[A[i]] = i
for j in range(40):
    for i in range(N):
        dist[j+1][i] = dist[j][i] + dist[j][(i + dist[j][i]) % N]
s = []
i = 0
while i < N * K:
    for j in range(41)[::-1]:
        if i + dist[j][i % N] <= N * K:
            i += dist[j][i % N]
            break
    else:
        s.append(A[i % N])
        i += 1
print(*s)

