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
def solve():
    N, K = map(int, input().split())
    As = list(map(int, input().split()))

    def getDistNexts(As):
        lenA = len(As)
        poss = dict()
        for i, A in enumerate(As):
            if A not in poss:
                poss[A] = i + lenA

        distNexts = [0]*(lenA)
        for i in reversed(range(lenA)):
            distNexts[i] = poss[As[i]] - i
            poss[As[i]] = i
        return distNexts

    distNexts = getDistNexts(As)

    NK = N*K
    maxD = (NK).bit_length() - 1

    dp = [[0]*(N) for _ in range(maxD+1)]
    for i in range(N):
        dp[0][i] = distNexts[i] + 1
    for d in range(1, maxD+1):
        for i in range(N):
            i2 = i + dp[d-1][i]
            dp[d][i] = i2 + dp[d-1][i2%N] - i

    iNow = 0
    dist = 0
    for d in reversed(range(maxD+1)):
        if dist+dp[d][iNow] < NK:
            dist += dp[d][iNow]
            iNow = dist%N

    Ss = []
    setS = set()
    for A in As[iNow:]:
        if A in setS:
            S = ''
            while S != A:
                S = Ss.pop()
                setS.remove(S)
        else:
            Ss.append(A)
            setS.add(A)

    if Ss:
        print(' '.join(map(str, Ss)))


solve()
