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)

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

dic = {}
for i in range(N):
    a = A[i]
    v = dic.get(a, None)
    if v is None:
        dic[a] = [i]
    else:
        v.append(i)

result = []
result_dic = {}
result_dic_index = {}
count = 0
loop = 0
while count < K:
    index = 0
    if count != 0:
        if result:
            a = result[index]
            v = dic.get(a)
            next_i = v[0]
            index = next_i + 1
            result.clear()
    while index < N:
        a = A[index]
        v = dic.get(a)
        next_i = -1
        for i in v:
            if i > index:
                next_i = i
                break
        if next_i == -1:
            result.append(a)
            index += 1
        else:
            index = next_i + 1
    tu = tuple(result)
    t = result_dic.get(tu, None)
    if t is None:
        result_dic[tu] = count
        result_dic_index[count] = tu
    else:
        loop = count
        break
    count += 1

answers = None
if loop == 0:
    answers = tu
else:
    index = (K - 1) % loop
    answers = result_dic_index[index]

for answer in answers:
    print(answer, end=" ")
print()