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()))

dict = {}
A_set = set(A)
for a in A_set:
    dict[a] = []
for i in range(N):
    dict[A[i]].append(i)

trans = {}
for a_list in dict.values():
    for i in range(len(a_list)):
        trans[a_list[i - 1]] = a_list[i]

k = 1
pos = 0
print_ans = 0
div_flag = 0
while True:
    new_pos = trans[pos]
    if new_pos <= pos:
        if k + 1 <= K:
            k += 1
            if new_pos + 1 < N:
                pos = new_pos + 1
            else:
                if div_flag == 0:
                    pos = 0
                    K = K % k
                    k = 1
                    div_flag = 1
                else:
                    print('')
                    break
        else:
            print_ans = 1
            break
    else:
        if new_pos + 1 < N:
            pos = new_pos + 1
        else:
            if div_flag == 0:
                pos = 0
                K = K % k
                k = 1
                div_flag = 1
            else:
                print('')
                break

if print_ans:
    ans = []
    i = pos
    while i < N:
        if trans[i] <= i:
            ans.append(A[i])
            i += 1
        else:
            i = trans[i] + 1
    print(' '.join(map(str, ans)))
