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;
typedef long long LL;
int a[200005];
int nt[200005];
int last[200005];
int main(){
    int n;
    LL k;
    scanf("%d%lld", &n, &k);
    for(int i=1;i<=n;i++){
        scanf("%d", &a[i]);
    }
    for(int i=n;i>=1;i--){
        nt[i] = last[a[i]];
        last[a[i]] = i;
    }
    memset(last, 0, sizeof(last));
    for(int i=1;i<=n;i++){
        if(last[a[i]] == 0) last[a[i]] = i;
        if(nt[i] == 0) nt[i] = last[a[i]];
    }
    int r = 1;
    int cur = 1;
    while(cur <= n){
        if(nt[cur] <= cur){
            r++;
            cur = nt[cur];
            cur++;
        }
        else{
            cur = nt[cur];
            cur++;
        }
    }
    k %= r;

    if(k != 0){
        cur = 1;
        k--;
        while(k > 0){
            if(nt[cur] <= cur){
                k--;
                cur = nt[cur];
                cur++;
            }
            else{
                cur = nt[cur];
                cur++;
            }
        }
        while(cur <= n){
            if(cur < nt[cur]){
                cur = nt[cur];
                cur++;
            }
            else{
                printf("%d ", a[cur]);
                cur++;
            }
        }
    }
}