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
import bisect
N, K, *A = [int(_) for _ in open(0).read().split()]
K -= 1
L = [[] for _ in range(2 * 10**5 + 1)]
for i, a in enumerate(A * 2):
    L[a] += [i]
before_next = [L[a][bisect.bisect(L[a], i)] for i, a in enumerate(A)]
first_cycle = [None] * N
now = 0
idx = 0
cycle = 0
while True:
    if first_cycle[now] is not None:
        break
    first_cycle[now] = cycle
    now = before_next[now] + 1
    dcycle, now = divmod(now, N)
    cycle += dcycle
cycle2 = cycle
cycle1 = first_cycle[now]
#K cycle目=cycle1+(K-cycle1)%(cycle2-cycle1) cycle目
K2 = cycle1 + (K - cycle1) % (cycle2 - cycle1)
if K2:
    f1 = f2 = 0
    for i in range(N - 1, -1, -1):
        if first_cycle[i] == K2 - 1:
            f1 = 1
            break
    for j in range(N - 1, -1, -1):
        if first_cycle[j] == K2:
            f2 = 1
            break
    if f2:
        B = A[j:]
    elif f1:
        B = A[i:] + A
else:
    B = A
ans = []
cnt = [0] * (2 * 10**5 + 1)
for a in B:
    if cnt[a] > 0:
        while True:
            cnt[ans.pop()] -= 1
            if cnt[a] == 0:
                break
    else:
        ans += [a]
        cnt[a] += 1
print(' '.join(map(str, ans)))
