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 math

# input
#
# n = 5
# k = 10
# a = [1, 2, 3, 2, 3]

n, k = map(int, input().split())
a = [int(ai) for ai in input().split()]

# make jumpto
#
# 0 -> 6 (5)
# 1 -> 4 (2)
# 2 -> 5 (2)
# 3 -> 7 (3)
# 4 -> 8 (3)

jumpto = [[-1] * n]
la = -1
li = -1
for (ca, ci) in sorted(zip(a, range(n))):
    if ca == la:
        jumpto[0][ci] = jumpto[0][li] + li - ci
        jumpto[0][li] = ci - li
    else:
        jumpto[0][ci] = n
    la = ca
    li = ci

# doubling jumpto
#
# 0 -> 6 ->  9 (8)
# 1 -> 4 ->  8 (6)
# 2 -> 5 -> 11 (8)
# 3 -> 7 -> 10 (6)
# 4 -> 8 -> 12 (7)
#
# 0 -> 6 ->  9 -> 13 -> 17  (16)
# 1 -> 4 ->  8 -> 12 -> 15  (13)
# 2 -> 5 -> 11 -> 14 -> 18  (15)
# 3 -> 7 -> 10 -> 16 -> 19  (15)
# 4 -> 8 -> 12 -> 15 -> 21  (16)

levels = int(math.log(k, 2))
for l in range(1, levels + 1):
    jumpto.append([-1] * n)
    for i in range(n):
        f = jumpto[l - 1][i]
        s = jumpto[l - 1][(i + f + 1) % n]
        jumpto[l][i] = f + 1 + s

# step1
s = 0
while True:
    jumped = False
    for l in range(levels, -1, -1):
        if s + jumpto[l][s % n] < n * k:
            s += jumpto[l][s % n] + 1
            jumped = True
            break
    if not jumped:
        break

# step2
ret = []
while s < n * k:
    if s + jumpto[0][s % n] < n * k:
        s = s + jumpto[0][s % n] + 1
    else:
        ret.append(str(a[s % n]))
        s += 1

print(' '.join(ret))
