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>
#include <map>
#include <set>

using namespace std;

int main()
{
    int N;
    long long K;
    cin>>N>>K;
    vector<int> A(N);
    for (int &a: A)
        cin>>a;

    vector<int> S(N, -1);
    map<int, int> M;
    for (int i=N-1; i>=0; i--)
        M[A[i]] = i;
    for (int i=N-1; i>=0; i--)
    {
        S[i] = M[A[i]];
        M[A[i]] = i;
    }

    int p = 0;
    long long k = 0;
    while (k<K-1)
    {

        if (S[p]<=p)
            k++;
        p = S[p]+1;
        if (p>=N)
        {
            p %= N;
            k++;
        }

        if (p==0)
        {
            long long t = (K-1)/k;
            k *= t;
        }
        //cout<<k<<" "<<p<<endl;
    }

    vector<int> ans;
    set<int> SS;

    for (int i=p; i<N; i++)
    {
        if (SS.count(A[i])>0)
        {
            while (ans.back()!=A[i])
            {
                SS.erase(ans.back());
                ans.pop_back();
            }
            ans.pop_back();
            SS.erase(A[i]);
        }
        else
        {
            ans.push_back(A[i]);
            SS.insert(A[i]);
        }
    }

    bool f = true;
    for (int a: ans)
    {
        cout<<(f?"":" ")<<a;
        f = false;
    }
    cout<<endl;
}
