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
from collections import defaultdict, Counter
from bisect import bisect_right, bisect_left

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

c = Counter(A)
target = []
d = defaultdict(list)

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

pos = 0
loop = 1
l = []

while pos < N:
    num = A[pos]
    
    pp = bisect_right(dd[num], pos)
    if pp < len(dd[num]):
        pos = dd[num][pp]+1
    else:
        pos = dd[num][0]+1            
        loop += 1
    l.append((num, pos, loop))

for v, pos, p in l:
    if (K-p)%loop==0:
        break

pos = pos if pos<N else 0
ans = []
while pos < N:
    num = A[pos]
    pp = bisect_right(dd[num], pos)
    if pp < len(dd[num]):
        pos = dd[num][pp]+1
    else:
        ans.append(num)
        pos += 1
print(*ans)
