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
# クソコードすぎる
N, K = map(int, input().split())
A = list(map(int, input().split()))
if N==1:
    if K%2==1:
        print(A[0])
    exit()
L = [-1] * (2*10**5+2)  # aを入れてindexを返す
Plus = [0]*N  # indexを入れて1か0
Next = [0]*N  # indexを入れてindex
for i, a in enumerate(A):
    l = L[a]
    if l==-1:
        L[a] = i
    else:
        Next[l] = i+1
        L[a] = i

if l!=-1:
    Next[l] = 0
    Plus[l] = 1
#print(Next)

for i, a in enumerate(A):
    l = L[a]  # あなたはどこから来たの
    if i <= l:
        Next[l] = i+1
        Plus[l] += 1
        L[a] = -1


#
# print(Next)
# print(Plus)

loop = Plus[0]
i = Next[0]
while i!=0:
    i_next = Next[i]
    if i_next==N:
        loop += 1
        i_next = 0
    #if i_next <= i:
    #    loop += 1
    loop += Plus[i]

    i = i_next
#
# print(loop)

TrueNext = Next.copy()
for i in range(N-1,-1,-1):
    p = Plus[i]
    if p==0:
        nn = TrueNext[i]
        if nn==N:
            nn = 0
        TrueNext[i] = TrueNext[nn]
#
# print(TrueNext)

k = K % loop
if k==0:
    exit()

start = 0
i=0
while i<k-1:
    if start==N:
        start=0
        i+=1
    if i==K-1:
        break
    start = TrueNext[start]
    i+=1
# print(start)

ans = []#[A[start]]
S = [0] * (2*10**5+2)
#S[ans[0]] = 1
for a in A[start:]:
    #print(a, ans)
    if S[a]==0:
        ans.append(a)
        S[a] = 1
    else:
        while S[a] != 0:
            a_ = ans.pop()
            S[a_] = 0
print(*ans)
