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<iostream>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<vector>
using namespace std;
typedef long long ll;
const int N=2e5+9;
int n,a[N];ll k;
vector<int>g[N];
int main(){
    ios::sync_with_stdio(0),cin.tie(0),cout.tie(0);
    cin>>n>>k;
    for(int i=1;i<=n;i++)cin>>a[i],g[a[i]].push_back(i);
    ll x=1,xh=1;
    while(1){
        int i=lower_bound(g[a[x]].begin(),g[a[x]].end(),x)-g[a[x]].begin();
        if(i==g[a[x]].size()-1)x=g[a[x]][0],xh++;else x=g[a[x]][i+1];
        if(x==n)break;
        x++;
    }
    //cout<<xh<<endl;
    ll y=k%xh;
    x=1;
    while(y){
        int i=lower_bound(g[a[x]].begin(),g[a[x]].end(),x)-g[a[x]].begin();
        if(i==g[a[x]].size()-1){
                if(y==1)cout<<a[x]<<" ";else x=g[a[x]][0],y--;
        }else x=g[a[x]][i+1];
        x++;if(x>n)y--,x=1;
    }
    cout<<endl;
    return 0;
}
