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 defaultdict
from bisect import bisect_right
import sys
input=sys.stdin.readline


def solve():
    N, K = map(int, input().split())
    *A, = map(int, input().split())

    dd = defaultdict(list)
    cc = defaultdict(list)

    for i, j in enumerate(A):
        dd[j].append(i)

    pos, loop = 0, 1
    ans = []

    while pos < N:
        num = A[pos]
        pp = bisect_right(dd[num], pos)
        if pp < len(dd[num]):
            pos = dd[num][pp]+1
        else:
            pos = dd[num][0]+1            
            loop += 1
        cc[loop].append(pos)

    pos = cc[K%loop][0] if cc[K%loop] else 0
    while pos < N:
        num = A[pos]
        pp = bisect_right(dd[num], pos)
        if pp < len(dd[num]):
            pos = dd[num][pp]+1
        else:
            ans.append(num)
            pos += 1
    print(*ans)


if __name__ == "__main__":
    solve()
