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,*a=map(int,open(0).read().split())
b=[[]for _ in range(max(a)+1)]
l=[]
for i,v in enumerate(a):
  b[v]+=i,
  l+=len(b[v]),
s=a[0]
i=c=0
while 1:
  t=b[s]
  m=len(t)
  j=l[i]
  c+=j==m
  i=t[j%m]+1
  if i==n:break
  s=a[i]
k%=c+1
s=a[0]
i=c=0
r=[]
while 1:
  t=b[s]
  m=len(t)
  j=l[i]
  f=j==m
  if c>k-2and f:
    r+=s,
    i+=1
  else:i=t[j%m]+1
  c+=f
  if i==n:break
  s=a[i]
print(*r)