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: Accepted)

from collections import deque
N, K = map(int, input().split())
A = list(map(int, input().split()))
next_step = [0] * N
memo = [-1] * (2*10**5)
cnt = 0
for i, a in enumerate(A+A):
    if memo[a-1] >= 0:
        if next_step[memo[a-1]%N]:
            continue
        next_step[memo[a-1]%N] = i - memo[a-1] + 1
        if next_step[memo[a-1]%N] == 0:
            pass
        cnt += 1
    if cnt == N:
        break
    memo[a-1] = i

j = 0
while True:
    if j + next_step[j%N] < N*K:
        j += next_step[j%N]
        if j%N == 0:
            j = max(j, N*K//j*j)
    else:
        break

q = deque()
memo = [-1] * (2*10**5)
cnt = 0
for k in range(j, N*K):
    a = A[k%N]
    if memo[a-1] < 0:
        q.append(a)
        memo[a-1] = cnt
        cnt += 1
    else:
        while True:
            b = q.pop()
            memo[b-1] = -1
            if b == a:
                break

print(*q)