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)

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

iNow = 0
dist = 0
hists = [-1] * N
hists[0] = 0
isSkipped = False
while dist + distNexts[iNow] + 1 < NK:
    dist += distNexts[iNow] + 1
    iNow = dist % N
    if not isSkipped and hists[iNow] != -1:
        period = dist - hists[iNow]
        dist += (NK-1-dist) // period * period
        isSkipped = True
    hists[iNow] = dist

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)))