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 sys
sys.setrecursionlimit(10**7)

readline = sys.stdin.buffer.readline
def readstr():return readline().rstrip().decode()
def readstrs():return list(readline().decode().split())
def readint():return int(readline())
def readints():return list(map(int,readline().split()))
def printrows(x):print('\n'.join(map(str,x)))
def printline(x):print(' '.join(map(str,x)))


import bisect

n,k = readints()

a = readints()

place = [[] for i in range(max(a)+1)]

for i,x in enumerate(a):
    place[x].append(i)

now = 0
i = 1
while k>1:
    x = a[now]
    if now >= place[x][-1]:
        i+=1
        k-=1
        now = place[x][0]+1
    else:
        now = place[x][bisect.bisect_right(place[x],now)] + 1
    if now == n:
        now = 0
        k-=1
        k%=i
        if k<1:
            k+=i

ans = []
while now <= n-1:
    x = a[now]
    if now >= place[x][-1]:
        ans.append(x)
        now += 1
    else:
        now = place[x][bisect.bisect_right(place[x],now)] + 1

printline(ans)
















