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 = map(int,input().split())
a = list(map(int,input().split()))

ind = [[] for _ in range(2*10**5 + 1)]
for i,num in enumerate(a):
    ind[num].append(i)

for i in range(1,2*10**5 + 1):
    if(ind[i]):
        ind[i].append(ind[i][0] + n)

before = []
cnt = 0
now = a[0]
while(True):
    right = bisect.bisect_right(ind[now], cnt%n)
    cnt += ind[now][right] - ind[now][right-1] + 1
    if(ind[now][right] >= n):
        before.append(ind[now][right-1])
    now = a[cnt%n]
    if(cnt%n == 0):
        break

if(cnt//n==1):
    print('')
    exit()

cyc = k%(cnt//n)

cnt = before[cyc-1]
ans = []
while(cnt < n):
    now = a[cnt]
    right = bisect.bisect_right(ind[now],cnt)
    if(ind[now][right] >= n):
        ans.append(now)
        cnt += 1
    else:
        cnt = ind[now][right] + 1

print(' '.join(map(str,ans)))