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

dic = {}
for i in range(n):
    if a[i] in dic:
        dic[a[i]].append(i)
    else:
        dic[a[i]] = [i]

zero = [-1 for i in range(n)]
for key, value in dic.items():
    num = len(value)
    for i in range(num-1):
        zero[value[i]] = value[i+1] - value[i] + 1
    zero[value[-1]] = n - value[-1] + value[0] + 1

lst = [zero]
while lst[-1][0] <+ n*k - 1:
    before = lst[-1]
    after = []
    for i in range(n):
        after.append(before[i] + before[(before[i]+i)%n])
    lst.append(after)
lst.pop()

i = 0
while lst != []:
    lsti = lst.pop()
    while True:
        if i + lsti[i%n] <= n*k - 1:
            i = i + lsti[i%n]
        else:
            break

i = i % n
nokori = a[i:]
lst = []
dic = {}
ko = 0
for i in range(len(nokori)):
    if nokori[i] not in dic:
        lst.append(nokori[i])
        dic[nokori[i]] = ko
        ko += 1
    else:
        lst = lst[:dic[nokori[i]]]
        dic = {}
        for j in range(len(lst)):
            dic[lst[j]] = j
        ko = len(lst)
print(*lst)