Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

3 2
1 2 3

Sample Output 1

2 3

In this case, X=(1,2,3,1,2,3).
We will perform the operations as follows:

i=0: s does not contain 1, so we add 1 to the end of s, resulting in s=(1).

i=1: s does not contain 2, so we add 2 to the end of s, resulting in s=(1,2).

i=2: s does not contain 3, so we add 3 to the end of s, resulting in s=(1,2,3).

i=3: s does contain 1, so we repeatedly delete the element at the end of s as long as s contains 1, which causes the following changes to s: (1,2,3)→(1,2)→(1)→().

i=4: s does not contain 2, so we add 2 to the end of s, resulting in s=(2).

i=5: s does not contain 3, so we add 3 to the end of s, resulting in s=(2,3).

Sample Input 2

5 10
1 2 3 2 3

Sample Output 2

3

Sample Input 3

6 1000000000000
1 1 2 2 3 3

Sample Output 3

s may be empty in the end.

Sample Input 4

11 97
3 1 4 1 5 9 2 6 5 3 5

Sample Output 4

9 2 6

Solution in Python (3.4.3) (judge verdict: Time Limit Exceeded)

import math

def main():
    N, K = list(map(int, input().split()))
    A = list(map(int, input().split()))

    dp = {}
    memo = set()
    # arrays = []
    # if len(set(A)) == len(A):
    #     if K % 2 == 0:
    #         print()
    #     else:
    #         print(*A, sep=" ")
    #     return
    
    L = []
    arrays = {}
    values = set()
    # K = min(K, K % 10 + 10)
    for k in range(K):
        for a in A:
            # print(L, memo)
            if a not in memo:
                i = len(L)
                L.append(a)
                dp[a] = i
                memo.add(a)
            else:
                i = dp[a]
                L = L[:i]
                memo = set(L)
                dp = {x: i for i,x in enumerate(L)}
        if len(L) == 0:
            s = " "
        else:
            s = " ".join(map(str,L))
        if s in values:
            loop = len(arrays)
            # print(loop)
            # print(arrays)
            print(arrays[(K-1) % loop])
            return
        else:
            arrays[k] = s
            values.add(s)



    print(*L, sep=" ")

if __name__ == "__main__":
    main()