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;

int main(){
    int N;
    int64_t K;
    cin >> N >> K;
    vector<int> A(N);
    for(int i=0; i<N; i++) cin >> A[i];
    
    int last[200001];
    static int64_t dub[60][200000];
    for(int i=2*N-1; i>=0; i--){
        if(i<N) dub[0][i] = last[A[i]] - i + 1;
        last[A[i%N]] = i;
    }
    const int64_t INF = 1e18;
    for(int k=0; k<59; k++) for(int i=0; i<N; i++){
        int64_t d1 = dub[k][i];
        int j = (i+d1) % N;
        dub[k+1][i] = min(INF, d1 + dub[k][j]);
    }
    int64_t done = 0;
    for(int k=59; k>=0; k--){
        int64_t d = dub[k][done%N];
        if(done + d <= N*K) done += d;
    }

    vector<int> ans;
    bitset<200001> exist;
    while(done < N*K){
        int a = A[done%N];
        if(exist[a]){
            while(exist[a]){
                exist[ans.back()] = 0;
                ans.pop_back();
            }
        }else{
            exist[a] = 1;
            ans.push_back(a);
        }
        done++;
    }
    int sz = ans.size();
    for(int i=0; i<sz; i++) cout << ans[i] << " \n"[i==sz-1];
}
