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;
typedef vector<ll> vec;
typedef vector<vec> mat;
typedef pair<ll,ll> pll;
const ll mod=1e9+7;
//const ll mod=998244353;
const ll inf=5e15;

const ll N=2e5+10;
vec fst(N),nxt(N),lst(N),ans(N),rep(N);
ll flag[N];

int main() {
  ll n,k;
  cin >> n >> k;
  vec a(n+1);
  for(ll i=1;i<=n;i++) {
    cin >> a[i];
    if(!fst[a[i]])fst[a[i]]=i;
  }
  nxt[n+1]=1;
  for(ll i=n;i;i--) {
    if(!lst[a[i]]) nxt[i]=fst[a[i]]+1;
    else nxt[i]=nxt[lst[a[i]]+1];
    lst[a[i]]=i;
  }
  ll cnt=0;
  for(ll i=1;!flag[i];i=nxt[i]) {
    flag[i]=1;
    rep[++cnt]=i;
  }
  memset(flag,0,sizeof(flag));
  ll top=0;
  for(ll i=rep[(k-1)%cnt+1];i<=n;i++) {
    if(!flag[a[i]]) ans[++top]=a[i],flag[a[i]]=1;
    else {
      while(ans[top+1]!=a[i]){
        flag[ans[top--]]=0;
      }
    }
  }
  for(ll i=1;i<=top;i++) {
    if(i!=1) cout << " ";
    cout << ans[i];
  }
  cout << endl;
}