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
input = sys.stdin.readline

N, K = map(int, input().split())
A = [int(i) for i in input().split()]

last = dict()
v = [-1] * N

for i, a in enumerate(A + A) :
    if a in last and last[a] < N :
        v[last[a]] = i + 1
    
    last[a] = i

dist = [-1] * N
cur = 0
cycle = 0
while dist[cur] < 0 :
    dist[cur] = cycle 
    cycle += v[cur] - cur
    cur = v[cur] % N

NK = N * K

m = NK % cycle
cur = v[cur] % N
s = 0
while m > dist[cur] > 0 :
    s = dist[cur]
    cur = v[cur] % N
m -= s

ret = []
seen = set()
for a in A[N-m:] :
    if a in seen :
        p = ret.pop()
        seen.remove(a)
        while p != a :
            seen.remove(p)
            p = ret.pop()
    else :
        ret.append(a)
        seen.add(a)
        
print(' '.join([str(i) for i in ret]))