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 rep(i, a, b) for(int i=(a) ; i<=(b) ; ++i)
#define mp make_pair
#define pii pair<int, int>
#define PB push_back
#define F first
#define S second
using namespace std;
const int N=200005;
int a[N], n, dd[N], same[N], dd2[N], b[N]; /// dd[i]: so i dau tien, same[i]: giong i sau i
long long k;

int main() {
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
    //freopen(".inp", "r", stdin);
    cin >> n >> k;
    rep(i, 1, n) {
        cin >> a[i];
        if(dd[a[i]]==0) dd[a[i]]=i;
        dd2[a[i]]=n+1;
    }

    same[n+1]=n+1;
    for(int i=n ; i ; --i) {
        same[i]=dd2[a[i]];
        dd2[a[i]]=i;
    }
    int ptr=1, num=1;
    while(1) {
        while(same[ptr]!=n+1) {
            ptr=same[ptr]+1;
        }

        if(ptr==n+1) break;
        b[num]=ptr;

        ptr=dd[a[ptr]]+1;
        ++num;
    }
    int remain=k%num;

    if(remain) {
        int xx=b[remain];
        while(xx<=n) {
            if(same[xx]==n+1) { cout << a[xx] << ' '; ++xx; }
            else xx=same[xx]+1;
        }

    }


    return 0;
}
