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
#include<cstdio>
#include<cstring>
int a[200005],n,b[200005];
int c[200005],d[200005];
long long int k;
int t=1;
int main(){
memset(c,0,sizeof(c));
scanf("%d%lld",&n,&k);
for(int i=1;i<=n;i++){
scanf("%d",&a[i]);
b[d[a[i]]]=i;
if(c[a[i]]==0)c[a[i]]=i;
b[i]=c[a[i]];
d[a[i]]=i;
}
if(n>1){
int p=1;
while(1){
if(b[p]<=p)t++;
p=b[p];
if(p==n)break;
p++;
}
k%=t;
p=1;
t=1;
while(t<=k){
if(b[p]<=p)
t++;
if(t<=k){
p=b[p];
p++;
}
}
for(int i=p;i<=n;i++)
if(b[i]>i)i=b[i];
else 
printf("%d ",a[i]);
}
else {
if(k%2)
printf("%d ",a[1]);
}
}