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 <vector>

using namespace std;

int main(){
    int N;
    long long K;
    cin >> N >> K;
    vector<int> A(N);
    vector<vector<int>> pos(200001);
    for(int i=0;i<N;i++){
        cin >> A[i];
        pos[A[i]].push_back(i);
    }
    vector<int> next(N);
    for(auto& v : pos){
        for(int i=0;i<v.size();i++){
            next[v[i]] = (v[(i+1)%v.size()] + 1) % N;
        }
    }
    vector<int> res;
    long long cycle = 0, p = 0;
    while(cycle < K){
        auto ncycle = cycle;
        if(next[p] == (p+1)%N) ++ncycle;
        if(next[p] <= p) ++ncycle;
        auto npos = next[p];
        if(ncycle >  K || (ncycle == K && npos > 0)){
            res.push_back(A[p]);
            if(p == N-1){
                p = 0;
                ++cycle;
            } else {
                p++;
            }
        } else {
            cycle = ncycle;
            p = npos;
            if(cycle < K && p == 0){
                K %= cycle;
                cycle = 0;
            }
        }
    }
    for(auto& t : res) cout << t << " ";
    cout << endl;
}