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;
#define LL long long
#define pb push_back
#define mp make_pair
#define fr first
#define sc second
const int N=200005;
vector<int> vp[N];
int a[N];
int binsrch(int i){
    int x=a[i];
    auto i1=upper_bound(vp[x].begin(),vp[x].end(),i);
    if (i1==vp[x].end()) return vp[x][0];
    else return *i1;
}
int work1(int n,LL K){
    int cnt=1;
    for (int i=1,ff=0;i!=1||!ff;ff=1){
        int j=binsrch(i);
        if (j<=i) cnt++;
        i=(j==n)?1:j+1;
    }

    return K%cnt;
}
void work2(int n,int K){
    if (!K) return;
    int i,cnt;
    for (i=1,cnt=1;cnt<K;){
        int j=binsrch(i);
        if (j<=i) cnt++;
        i=j+1;
    }
    for (;i<=n;){
        for (;i<=n;){
            int j=binsrch(i);
            if (j<=i) break;
            i=j+1;
        }
        if (i<=n) printf("%d ",a[i++]);
    }
}
int main(){
   // freopen("in.txt","r",stdin);
   // freopen("out.txt","w",stdout);
    int n,m;LL K0;cin>>n>>K0;
    for (int i=1;i<=n;i++){
        scanf("%d",a+i);
        vp[a[i]].pb(i);
    }
  //  cout<<binsrch(1)<<endl;
    m=work1(n,K0);
    work2(n,m);

    return 0;
}
