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

readline = sys.stdin.readline
MOD = 10 ** 9 + 7
INF = float('INF')
sys.setrecursionlimit(10 ** 5)


def main():
    from collections import defaultdict

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

    c = N * K
    b = 0
    while 2 ** b < c:
        b += 1

    doubling = [[0] * N for _ in range(b + 1)]

    idx = defaultdict(list)
    for i, x in enumerate(A):
        idx[x].append(i)

    for i in range(1, 200001):
        d = idx[i]
        l = len(d)
        for j in range(l):
            cur = d[j]
            nx = d[(j + 1) % l]
            if nx <= cur:
                doubling[0][cur] = N - (cur - nx) + 1
            else:
                doubling[0][cur] = nx - cur + 1

    for i in range(1, b + 1):
        for j in range(N):
            p = doubling[i - 1][j]
            doubling[i][j] = p + doubling[i - 1][(j + p) % N]

    cnt = 0
    cur = 0
    while c - cnt > 200000:
        for i in range(b, -1, -1):
            if cnt + doubling[i][cur] < c:
                cnt += doubling[i][cur]
                cur = cnt % N
                break

    rem = c - cnt
    res = []
    res_set = set()

    while rem > 0:
        num = A[cur]
        if num in res_set:
            while True:
                back = res[-1]
                res.pop()
                res_set.discard(back)
                if back == num:
                    break
        else:
            res.append(num)
            res_set.add(num)
        rem -= 1
        cur += 1
        cur %= N

    print(*res)


if __name__ == '__main__':
    main()
