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>

using namespace std;

int main()
{
    long long n; long long k; cin >> n >> k;
    long long arr[202020]; for(long long i = 0; i < n; ++i) cin >> arr[i];

    long long dis[202020], chc[202020];
    for(long long &i : dis) i = -1; for(long long &i : chc) i = -1;

    for(long long i = n - 1; i >= 0; --i)
    {
        if(chc[arr[i]] != -1) dis[i] = chc[arr[i]] - i + 1;
        chc[arr[i]] = i;
    }
    for(long long i = n - 1; i >= 0; --i)
        if(dis[i] == -1) dis[i] = n + chc[arr[i]] - i + 1;

    long long cyc[202020]; for(long long &i : cyc) i = -1;
    long long pt = 0, cnt = 0;
    while(cyc[pt] == -1)
    {
        cyc[pt] = cnt;
        cnt += dis[pt];
        pt = cnt % n;
    }

    long long ini = cyc[pt];
    long long len = cnt - cyc[pt];

    long long ori = k * n;
    if(ori >= ini) ori -= ini;
    ori %= len;

    while(ori)
    {
        if(ori >= dis[pt]) ori -= dis[pt];
        else
        {
            cout << arr[pt] << ' ';
            --ori;
        }
        pt = n - ((ori - 1) % n + 1);
    }

    return 0;
}
