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;

using i64 = int64_t;

int main(){
    i64 n, k;
    cin >> n >> k;
    vector<i64> v, nxt(n, -1), num2idx(200001, -1);
    for(int i=0;i<n;++i){
        i64 a;
        cin >> a;
        v.push_back(a);
        if(num2idx[a] != -1)nxt[num2idx[a]] = i;
        num2idx[a] = i;
    }
    for(int i=0;i<n;++i){
        if(nxt[num2idx[v[i]]] != -1)continue;
        nxt[num2idx[v[i]]] = i;
    }

    i64 a = 0, period = 0;
    do{
        i64 b = nxt[a];
        if(b <= a)period++;
        b = (b+1) % n;
        if(b == 0)period++;
        a = b;
    }while(a != 0);

    i64 m = k % period - 1;
    if(m < 0)m += period;
    //cerr << period << " " << m << endl;
    a = 0;
    while(m > 0){
        i64 b = nxt[a];
        if(b <= a)m--;
        b = (b+1) % n;
        if(b == 0)m--;
        a = b;
        //cerr << a << " " << m << endl;
    }

    vector<i64> ans;
    for(;a<n;++a){
        if(nxt[a] > a){
            a = nxt[a];
            continue;
        }
        ans.push_back(v[a]);
    }
    for(int i=0;i<(int)ans.size();++i){
        if(i)cout << " ";
        cout << ans[i];
    }
    cout << endl;

    return 0;
}