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())
A = [int(a) for a in input().split()]
M = 200100
P = [-1 for i in range(M)]
NE = [-1 for a in range(N)]
for i in range(N):
    if P[A[i]] >= 0 and NE[P[A[i]]] < 0:
        NE[P[A[i]]] = i
    P[A[i]] = i
for i in range(N):
    if P[A[i]] >= 0 and NE[P[A[i]]] < 0:
        NE[P[A[i]]] = i
    P[A[i]] = i

i = 0
c = 1
while True:
    if NE[i] <= i: c += 1
    i = (NE[i] + 1) % N
    if i == 0:
        break
K %= c
ANS = []
i = 0
while K:
    while NE[i] > i:
        i = (NE[i] + 1) % N
    if K >= 2:
        i = (NE[i] + 1) % N
        K -= 1
    else:
        break
while i < N:
    if NE[i] > i:
        i = NE[i] + 1
    else:
        ANS.append(A[i])
        i += 1
print(*ANS)