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<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int MOD=1e9+7;
const int INF=1e9;

int main(){
    ll n,k;
    cin>>n>>k;
    int a[n];
    for(int i=0;i<n;i++){
        cin>>a[i];
    }
    int prev[200001];
    for(int i=n-1;i>=0;i--){
        prev[a[i]]=i;
    }
    int next[n];
    for(int i=n-1;i>=0;i--){
        next[i]=prev[a[i]];
        prev[a[i]]=i;
    }
    int cnt=1,now=0;
    do{
        if(now>=next[now])cnt++;
        now=(next[now]+1)%n;
    }while(now!=0);
    int r=k%cnt;
    if(r==0){
        cout<<endl;
        return 0;
    }
    cnt=1,now=0;
    while(cnt!=r){
        if(now>=next[now])cnt++;
        now=next[now]+1;
    }
    for(int i=now;i<n;i++){
        if(i<next[i]){
            i=next[i];
        }
        else{
            cout<<a[i]<<" ";
        }
    }
    cout<<endl;
}