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>
#define int long long
using namespace std;
const int maxn = 2e5 + 7;
const int inf = 1e18;
int n,m, a[maxn * 2], cur[maxn * 2];
int nxt[60][maxn];

int32_t main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    if(fopen("test.inp", "r")) freopen("test.inp", "r", stdin), freopen("test.out", "w", stdout);
    cin >> n >> m;
    m *= n;
    for(int i = 0; i < n; i++)
    {
        cin >> a[i];
        a[n + i] = a[i];
    }
    for(int i = 2 * n - 1; i >= 0; i--)
    {
        if(i < n) nxt[0][i] = cur[a[i]] - i + 1;
        cur[a[i]] = i;
    }
    for(int len = 1; len < 60; len++)
    {
        for(int i = 0; i < n; i++)
        {
            int gau = (i + nxt[len - 1][i]) % n;
            nxt[len][i] = min(inf, nxt[len - 1][i] + nxt[len - 1][gau]);
        }
    }
    int gau = 0;
    for(int i = 59; i >= 0; i--)
    {
        if(gau + nxt[i][gau % n] <= m)
        {
            gau += nxt[i][gau % n];
        }
    }
    if(gau == m) return 0;
    gau %= n;
    while(gau < n)
    {
        if(nxt[0][gau] + gau > n)
        {
            cout << a[gau++] << ' ';
        }
        else gau += nxt[0][gau];
    }
}
