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
#  --*-coding:utf-8-*--

def main():
    N, K = map(int, input().split())
    A = list(map(int, input().split()))
    
    B = [None]*N
    firstPos = {}
    lastPos = {}

    for p, a in enumerate(A):
        if a in lastPos:
            B[lastPos[a]] = p
            B[p] = firstPos[a]
        else:
            firstPos[a] = p
            B[p] = p

        lastPos[a] = p

    C = [None]*N
    for p, b in enumerate(B):
        c = (b - p)%N
        if c == 0:
            c = N

        C[p] = c + 1

    cycle = C[0]
    nextPos = cycle%N

    while nextPos != 0:
        cycle += C[nextPos]
        nextPos = (nextPos + C[nextPos])%N

    r = N*K%cycle
    ans = []

    while r > 0:
        while r >= C[(-r)%N]:
            r -= C[(-r)%N]

        if r > 0:
            ans.append(A[(-r)%N])
            r -= 1
        
    print(' '.join(map(str, ans)))


if __name__ == '__main__':
    main()
