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
#!/usr/bin/env python
# coding: utf-8

# In[1]:


N, K = map(int, input().split())
A = [int(x) for x in input().split()]


# In[2]:


kioku = {}
saisyo = {}
idou = {}

for i in range(N):
    if A[i] in kioku:
        idou[kioku.pop(A[i])] = i
    kioku[A[i]] = i
    if A[i] not in saisyo:
        saisyo[A[i]] = i

    


# In[3]:


# kioku


# In[4]:


# saisyo


# In[5]:


# idou


# In[6]:


i = 0
ret = []
while True:
    if i in idou:
        i = idou[i]
    else:
        ret.append(i)
        i = saisyo[A[i]]
    if i == N - 1:
        i = 0
        break
    else:
        i += 1


# In[7]:


# 3-35 -59- -92- -26- -65-5 31415926535


# In[8]:


# ret


# In[ ]:





# In[ ]:





# In[9]:


loop = len(ret) + 1
if K % loop != 0:
#     print(ret[K % loop - 1])
#     print(A[ret[K % loop - 1]:])
    i = ret[K % loop - 1]
    ans = []
    while i <= N - 1:
        if i in idou:
            i = idou[i]
        else:
            ans.append(A[i])
        i += 1
    print(' '.join(map(str, ans)))


# In[ ]:




