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
def main():
    import bisect
    n,k=map(int,input().split())
    x=list(map(int,input().split()))
    d=dict()
    for j,i in enumerate(x):
        if i in d.keys():
            d[i].append(j)
        else:
            d[i]=[j]
    first_word=[""]
    
    def operation(temp_operated,temp_operator):
        l=[i for i in temp_operated]
        s=set(temp_operated)
        for i in temp_operator:
            if i in s:
                while True:
                    if l[-1]!=i:
                        l.pop()
                    else:
                        l.pop()
                        s=set(l)
                        break
            else:
                l.append(i)
                s.add(i)
        return l
    
    if operation("",x)!=[]:
        first_word.append(operation("",x)[0])
    flag=0

    while True:
        w=first_word[-1]
        if w=="":
            break
        t=d[w][0]
        if t==n-1:
            break
        while True:
            ww=x[t+1]
            temp=bisect.bisect_right(d[ww],t+1)
            if temp>=len(d[ww]):
                first_word.append(ww)
                break
            else:
                t=d[ww][temp]
                if t==n-1:
                    flag=1
                    break
        if flag==1:
            break
    
    l=len(first_word)
    k=k%l
    if len(first_word)==1:
        print("")
    elif k-1==0:
        print(*operation("",x))
    else:
        print(*operation("",x[d[first_word[k-1]][0]+1:]))

main()