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

a = list(set(A))
a.sort()
R = {}
for i in range(len(a)):
  R[a[i]] = i

n = len(a)
L = [[] for _ in range(n)]
P = [[0, 0] for _ in range(N)]
for i in range(N):
  P[i][0] = R[A[i]]
  P[i][1] = len(L[R[A[i]]])
  L[R[A[i]]].append(i)

s = [R[A[0]], 0]
D = [0]

while True:
  while s[1] < len(L[s[0]]) - 1:
    t = L[s[0]][s[1] + 1]
    if t != N - 1:
      s = P[t + 1]
    else:
      break
  else:
    if L[s[0]][0] == N - 1:
      D.append(N)
      break
    s = P[L[s[0]][0] + 1]
    D.append(L[s[0]][s[1]])
    continue
  break

M = len(D)
m = (K - 1) % M

if m == M - 1:
  print()
  exit()
ans = []
s = P[D[m]]
t = L[s[0]][s[1]]

while t != N:
  if s[1] == len(L[s[0]]) - 1:
    ans.append(A[t])
    t += 1
  else:
    t = L[s[0]][s[1] + 1] + 1
  if t == N:
    break
  s = P[t]

print(" ".join(list(map(str, ans))))