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 sys
input = sys.stdin.readline

N, K = (int(i) for i in input().split())
A = [int(i) for i in input().split()]
L = [0]*N
P = [-1]*(2*10**5+1)
for i in range(2*N):
    j = i%N
    a = A[j]
    if P[a] == -1:
        P[a] = i
    else:
        L[P[a]] = j
        P[a] = j
s = 0
start = 0
v = [True]*N
h = [(0, 0)]
h_app = h.append
while v[start]:
    v[start] = False
    if start < L[start]:
        s += (L[start] - start +1)
    else:
        s += (L[start] - start +N +1)
    start = (L[start]+1)%N
    h_app((s, start))

r = (N*K)%s
import bisect
if r == 0:
    print("")
else:
    res = bisect.bisect(h, (r, 10**10))-1
    s, start = h[res]
    s = r-s
    ans = []
    P = [-1]*(2*10**5+1)
    if s:
        cou = 0
        for i in range(s):
            if P[A[(start+i)%N]] == -1:
                P[A[(start+i)%N]] = cou
                ans.append(str(A[(start+i)%N]))
            else:
                sr = P[A[(start+i)%N]]
                P[A[(start+i)%N]] = -1
                for j in range(cou-sr):
                    a = ans.pop()
                    P[int(a)] = -1
                cou = sr-1
            cou += 1
    print(" ".join(ans))
