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_left, bisect_right


def main():
    N, K = map(int, input().split())
    A = list(map(int, input().split()))
    idx = [[] for _ in range(int(2e5+1))]
    for i in range(N):
        idx[A[i]].append(i)
    pos = 0
    empty = []
    visited = set()
    while pos == 0 or pos % N != 0:
        empty.append(pos)
        visited.add(pos % N)
        a = A[pos % N]
        nxt = bisect_right(idx[a], pos % N) % len(idx[a])
        npos = idx[a][nxt] + (pos//N) * N
        if npos <= pos:
            npos += N
        pos = npos + 1
    goal = N * K % pos
    cur = empty[max(0, bisect_right(empty, goal) - 1)]
    #print(cur, goal)
    ans = []
    seen = set()
    while cur < goal:
        i = cur % N
        a = A[i]
        nxt = bisect_right(idx[a], cur % N) % len(idx[a])
        ncur = idx[a][nxt] + (cur//N) * N
        if ncur <= cur:
            ncur += N
        if ncur < goal:
            cur = ncur + 1
        else:
            ans += [a]
            cur = cur + 1
    print(*ans)


if __name__ == "__main__":
    main()
