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()))
b = a + a
to = [-1] * n
num = [-1] * (2 * 10 ** 5 + 1)
for i, x in enumerate(b):
    if 0 <= num[x] < n:
        to[num[x]] = i + 1
    num[x] = i

c, now = 1, 0
check = 0
while now != n:
    v = to[now]
    if v > n:
        c += 1
        v -= n

    now = v



k %= c
now = 0
while k > 1:
    v = to[now]
    if v > n:
        k -= 1
        v -= n

    now = v

ans = []

while now < n:
    if to[now] < n:
        now = to[now]
    elif to[now] == n:
        break
    else:
        ans.append(a[now])
        now += 1

print(*ans)
