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.

Examples

Input

3 2
1 2 3


Output

2 3


Input

5 10
1 2 3 2 3


Output

3


Input

6 1000000000000
1 1 2 2 3 3


Output




Input

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


Output

9 2 6
import bisect
n, k = map(int, input().split())
alist = list(map(int, input().split()))
positions = [[] for i in range(200002)]
for i in range(n):
    positions[alist[i]].append(i)
visited = [0] * n
lastList = []
nextP = 0
times =0
while True:
    num = alist[nextP]
    if len(positions[num]) == 1:
        lastList.append(nextP)
        visited[nextP] = times
        times += 1
        nextP += 1
        if nextP == n:
            break
    else:
        nextIn = bisect.bisect_right(positions[num], nextP)
        if nextIn == len(positions[num]):
            lastList.append(nextP)
            visited[nextP] = times
            times += 1
            nextP = positions[num][0] + 1
        else:
            nextP = positions[num][nextIn] + 1
            if nextP == n:
                break
if times != 0:
    loopIn = k % (times + 1)
    if loopIn != 0:
        loopIn -= 1
        lastIn = lastList[loopIn]
        result = []
        while True:
            num = alist[lastIn]
            nextIn = bisect.bisect_right(positions[num], lastIn)
            if nextIn == len(positions[num]):
                result.append(num)
                lastIn += 1
            else:
                lastIn = positions[num][nextIn] + 1
            if lastIn == n:
                break
        if len(result) > 0:
            print(' '.join(map(str, result)))
