Problem: For a given array $a_1, a_2, a_3, ... , a_N$ of $N$ elements and an integer $L$, find the minimum of each possible sub-arrays with size $L$ and print them from the beginning. For example, for an array $\\{1, 7, 7, 4, 8, 1, 6\\}$ and $L = 3$, the possible sub-arrays with size $L = 3$ includes $\\{1, 7, 7\\}$, $\\{7, 7, 4\\}$, $\\{7, 4, 8\\}$, $\\{4, 8, 1\\}$, $\\{8, 1, 6\\}$ and the minimum of each sub-array is 1, 4, 4, 1, 1 respectively.

Constraints

* $1 \leq N \leq 10^6$
* $1 \leq L \leq 10^6$
* $1 \leq a_i \leq 10^9$
* $L \leq N$

Input

The input is given in the following format.

$N$ $L$
$a_1$ $a_2$ ... $a_N$

Output

Print a sequence of the minimum in a line. Print a space character between adjacent elements.

Example

Input

7 3
1 7 7 4 8 1 6


Output

1 4 4 1 1

Solution (in CPP):

Solution:
#include <cstdio>
#include <utility>
#include <deque>
using namespace std;
using pii = pair<int, int>;

int main() {
    int N, L; scanf("%d%d", &N, &L);
    
    deque<pii> deq;
    for(int i=0; i<N; i++) {
        int val; scanf("%d", &val);
        int lim = i - L + 1;

        while(deq.size()) {
            pii elem = deq.front();
            if(elem.second < lim || elem.first > val) {
                deq.pop_front();
            }
            else break;
        }
        while(deq.size()) {
            pii elem = deq.back();
            if(elem.second < lim || elem.first > val) {
                deq.pop_back();
            }
            else break;
        }
        deq.push_back(make_pair(val, i));
        
        if(i+1 >= L) printf("%d%c", deq.front().first, (i+1==N ? '\n' : ' '));
    }
    return 0;
}