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:
//final_report
#include<iostream>
#include<cstdio>
#include<vector>
#include<algorithm>
#include<cstring>
#include<stdio.h>
#include<fstream>
#include<stdlib.h>
#include<math.h> 
#include<queue>
#include<string.h>
#include<stack>
#include <climits>

#define INF INT_MAX

using namespace std;


int n=0;
int A[30000000];

void initRMQ(int size){
	n=1;
	while(n<=size){
		n*=2;
	}
	for(int i=0;i<2*n-1-1;i++){
		A[i]=INF;
	}
}

void updata(int k,int x){
	k+=n-1;
	A[k]=x;
	while(k>0){
		k=(k-1)/2;
		A[k]=min(A[k*2+1],A[k*2+2]);
	}
}

int query(int x,int y,int k,int l,int n){
	if(n<=x||y<=l){
		return INF;
	}
	if(x<=l&&n<=y){
		return A[k];
	}
	int v1=query(x,y,k*2+1,l,(l+n)/2);
	int v2=query(x,y,k*2+2,(l+n)/2,n);
	return min(v1,v2);
}

int query2(int x,int y){
	return query(x,y,0,0,n);
}

int main(){
	int N,l,a;
	cin>>N>>l;

	initRMQ(N);

	for(int i=0;i<N;i++){
		cin>>a;
		updata(i,a);
	}
	int j=0;
	while(1){
		cout <<query2(j, j+l);
		if(j+l-1==N-1)break;
		cout<<' ';
		j++;
	}
	cout<<endl;

	return 0;

}