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
N, K = map(int, input().split())
As = list(map(int, input().split()))
M = [[] for i in range(200001)]
for i, a in enumerate(As):
  M[a].append(i)
S = []
for i, a in enumerate(As):
  l = M[a]
  index = l.index(i)
  if index+1 == len(l):
    n = l[0]+N
  else:
    n = l[index+1]
  S.append(n+1-i)
#print(S)
p = 0
while True:
  p = p+S[p%N]
  if p%N == 0:
    break
count = p//N
#print(count)
K = K%count
#print(K)
p = 0
s = []
while p < N*K:
  q = p+S[p%N]
  if q > N*K:
    s.append(As[p%N])
    p = p+1
  else:
    p = q
print(" ".join(map(str, s)))
