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

if n == 1:
    print(*(aaa * (k % 2)))
    exit()

follow = [-1] * n
tmp = {}
fix = 0
while True:
    for i in range(n):
        a = aaa[i]
        if a in tmp:
            follow[tmp[a]] = (i + 1) % n
            tmp[a] = i
            fix += 1
        else:
            tmp[a] = i
    if fix >= n:
        break
# print(follow)
loop = 1
i = 0
while True:
    j = follow[i]
    if j == 0:
        if i == n - 1:
            loop += 1
        break
    if i + 1 >= j:
        loop += 1
    # print(i, j, loop)
    i = j

k %= loop
if k == 0:
    print()
    exit()

# print(k, loop)


def simulate(aaa, s, follow):
    tmp = []
    exs = set()
    for a in aaa[s:]:
        if a in exs:
            while True:
                b = tmp.pop()
                exs.remove(b)
                if a == b:
                    break
        else:
            tmp.append(a)
            exs.add(a)

    # i = s
    # while i != 0:
    #     j = follow[i]
    #     if j == 0:
    #         if i == n - 1:
    #             tmp.append(aaa[i])
    #         break
    #     elif i + 1 >= j:
    #         tmp.append(aaa[i])
    #         i = (i + 1) % n
    #     else:
    #         i = j
    return tmp


# print(simulate(aaa * 5, 0, follow))
# print(simulate(aaa * 6, 0, follow))

i = 0
loop = 1
while loop <= k:
    j = follow[i]
    if i + 1 >= j:
        if loop == k:
            print(*simulate(aaa, i, follow))
            break
        loop += 1
    i = j
