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 bisect import bisect_right
n, k = map(int, input().split())
a = [int(x) for x in input().split()]

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


def simulate(k):
    if k == 0:
        return 0, []
    lap = 1
    res = [0]
    while True:
        s = res.pop()
        nxt = d[a[s]][bisect_right(d[a[s]], s) % len(d[a[s]])] + 1
        if nxt == n:
            if lap == k and s == n-1:
                res.append(s)
            if s == n-1:
                lap += 1
            return lap, res
        elif nxt <= s+1:
            if lap == k:
                res.append(s)
                if s == n-1:
                    return lap, res
                res.append(s+1)
                if s+1 == n-1:
                    return lap, res
            else:
                res.append(nxt)
                lap += 1
        else:  # s+1 < nxt
            s = nxt
            res.append(s)
    return 0


period, ans = simulate(k)

if period != k:
    lap, ans = simulate(k % period)

print(*[a[x] for x in ans])
