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
#17:43
n,k = map(int,input().split())
a = list(map(lambda x: int(x)-1, input().split()))
mx = max(a) + 1
num = [[] for _ in range(mx)]
leg = [0 for _ in range(mx)]
for i in range(n):
  num[a[i]].append(i)
  leg[a[i]] += 1
#print(num)
nex = [0 for _ in range(n)]
for j in range(mx):
  nu = num[j]
  le = leg[j]
  for li in range(le-1):
    nex[nu[li]] = nu[li+1]+1
  if nu:
    nex[nu[-1]] = nu[0]+n+1
#print(nex)
unit = 0
now = 0
while True:
  tmp = nex[now]
  unit += tmp // n
  now = tmp % n
  #print(tmp,now)
  if now == 0:
    break
#print(unit)
k %= unit
k *= n
#print(k)
if k == 0:
  exit()
while True:
  tmp = nex[now]
  if k - (tmp-now) > 0:
    k -= tmp - now
    now = tmp % n
  else:
    ans = a[-k:]
    break
  #print(k)
l = len(ans)
seen = [0 for _ in range(mx)]
ans2 = []
for li in range(l):
  if seen[ans[li]] == 1:
    while True:
      p = ans2.pop()
      seen[p] = 0
      if p == ans[li]:
        break
  else:
    ans2.append(ans[li])
    seen[ans[li]] = 1
print(' '.join(map(lambda x:str(x+1),ans2)))