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: Wrong Answer)

from collections import defaultdict
from bisect import bisect

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

indices = defaultdict(list)
for i,a in enumerate(A):
    indices[a].append(i)

memo = [False]*N
memo[0] = True
trace = [0]
cnt = [0]
while True:
    i = trace[-1]
    c = cnt[-1]
    l = indices[A[i]]
    j = (l[bisect(l,i)%len(l)]+1)%N
    if j <= i+1:
        c += 1
    trace.append(j)
    cnt.append(c)
    if memo[j]:
        break
    else:
        memo[j] = True

i = trace.index(trace[-1])

period = cnt[-1] - cnt[i]
K -= 1
if K > cnt[i]:
    K = (K-cnt[i])%period + cnt[i]
head = trace[bisect(cnt, K)-1]

ans = []
cur = head
while cur < N:
    l = indices[A[cur]]
    j = bisect(l, cur)
    if j == len(l):
        ans.append(cur)
        cur += 1
    else:
        cur = l[j]+1

print(*(A[i] for i in ans))