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
sys.setrecursionlimit(pow(10, 6))

def main():
    n, k = map(int, input().split())
    a = list(map(int, input().split()))
    na = [-1 for _ in range(2*n)]
    nk = n * k

    prevai = {}
    for i, _a in enumerate(a+a):
        if _a in prevai:
            na[prevai[_a]] = (i-prevai[_a])%n + 1
            if na[prevai[_a]] == 1:
                na[prevai[_a]] = n+1
        prevai[_a] = i

    doubling = [[0 for _ in range(n)] for _ in range(61)]
    for i in range(n):
        doubling[0][i] = na[i]
    for i in range(1, 61):
        for j in range(n):
            doubling[i][j] = min(doubling[i-1][j] + doubling[i-1][(j+doubling[i-1][j])%n], nk+5)

    tmp = 0
    for i in range(60, -1, -1):
        if nk - tmp >= doubling[i][tmp%n]:
            tmp += doubling[i][tmp%n]

    if tmp == nk:
        return
    
    ans  = []
    adict = {}
    for i in range(tmp%n, n):
        if a[i] in adict and adict[a[i]] > 0:
            while True:
                _a = ans.pop()
                adict[_a] = 0
                if _a == a[i]:
                    break
        else:
            ans.append(a[i])
            adict[a[i]] = 1
    print(*ans)


if __name__ == '__main__':
    main()
