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
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)

N, K = mapint()
As = list(mapint())
double_As = As*2
idx_dic = {}
idx_lis = [N+1]*(2*N)
for i in range(N*2-1, -1, -1):
    a = double_As[i]
    if a in idx_dic:
        idx_lis[i] = idx_dic[a]+1
    idx_dic[a] = i
doubling = [[0]*N for _ in range(60)]
accum = [[0]*N for _ in range(60)]
doubling[0] = [i%N for i in idx_lis[:N]]
accum[0] = [a-i for i, a in enumerate(idx_lis[:N])]
for i in range(1, 60):
    for j in range(N):
        doubling[i][j] = doubling[i-1][doubling[i-1][j]]
        accum[i][j] = accum[i-1][j] + accum[i-1][doubling[i-1][j]]
now = 0
cum = 0
cnt = 0
for i in range(59, -1, -1):
    if cum + accum[i][now]>N*K:
        continue
    else:
        cum += accum[i][now]
        now = doubling[i][now]
ans = []
while cum<N*K:
    if cum+accum[0][now]<=N*K:
        cum += accum[0][now]
        now = doubling[0][now]
    else:
        ans.append(As[now])
        now += 1
        cum += 1
print(*ans)
