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

d = {}
for i, a in enumerate(A):
    if a in d:
        d[a].append(i)
    else:
        d[a] = [i]

loop_cnt = 0
sp = []
p = 0
fp = 1
top = A[0]
while True:
    loop_cnt += 1
    while fp < N:
        np = bisect.bisect_left(d[top], fp)
        if np < len(d[top]):
            p = d[top][np] + 1
            fp = p+1
            if p < N:
                top = A[p]
        else:
            break
    if p >= N:
        break
    top = A[p]
    sp.append(p)
    fp = 0

k = K % loop_cnt - 1
if k == -1:
    exit()
p = sp[k]
s = []
while p < N:
    top = A[p]
    while True:
        np = bisect.bisect_left(d[top], p+1)
        if np < len(d[top]):
            p = d[top][np] + 1
            if p < N:
                top = A[p]
        else:
            break
    if p < N:
        s.append(top)
        p += 1

print(' '.join(map(str, s)))
