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
from collections import Counter
N, K = map(int, input().split())
A = list(map(int, input().split()))

C = Counter()
table = [None]*N
for i in range(N-1, -1, -1):
    a = A[i]
    C[a] = i
for i in range(N-1, -1, -1):
    a = A[i]
    table[i] = C[a]
    C[a] = i
cost = [1 + table[i] - i if table[i] > i else 1+ table[i] - i + N for i in range(N)] 
table = [(1+t)%N for t in table]
loop = 0
st = 0
en = None
while en != 0:
    en = table[st]
    loop += cost[st]
    st = en
K = (N*K) % loop
st = 0
while K - cost[st] >= 0:
    K -= cost[st]
    st = table[st]
sS = set()
S = []
for i in range(K):
    a = A[(st+i)%N]
    if a in sS:
        sS.remove(a)
        while S[-1] != a:
            sS.remove(S.pop())
        S.pop()
    else:
        S.append(a)
        sS.add(a)
print(*S)
