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<bits/stdc++.h>
using namespace std;
using Int = long long;

template <typename T,typename E,typename F,typename G>
struct SegmentTree{
  int n;
  F f;
  G g;
  T ti;
  vector<T> dat;
  SegmentTree(){};
  SegmentTree(int n_,F f,G g,T ti):
    f(f),g(g),ti(ti){
    init(n_);
  }
  void init(int n_){
    n=1;
    while(n<n_) n*=2;
    dat.assign(2*n-1,ti);
  }
  void build(int n_, vector<T> v){
    for(int i=0;i<n_;i++) dat[i+n-1]=v[i];
    for(int i=n-2;i>=0;i--)
      dat[i]=f(dat[i*2+1],dat[i*2+2]);
  }
  void update(int k,E a){
    k+=n-1;
    dat[k]=g(dat[k],a);
    while(k>0){
      k=(k-1)/2;
      dat[k]=f(dat[k*2+1],dat[k*2+2]);
    }
  }
  inline T query(int a,int b){
    T vl=ti,vr=ti;
    for(int l=a+n,r=b+n;l<r;l>>=1,r>>=1) {
      if(l&1) vl=f(vl,dat[(l++)-1]);
      if(r&1) vr=f(dat[(--r)-1],vr);
    }
    return f(vl,vr);
  }

  int find(int a,int b,function<bool(T)> &check,int k,int l,int r){
    if(!check(dat[k])||r<=a||b<=l) return -1;
    if(k>=n-1) return k-(n-1);
    int m=(l+r)>>1;
    int vl=find(a,b,check,k*2+1,l,m);
    if(~vl) return vl;
    return find(a,b,check,k*2+2,m,r);
  }
  
  int find(int a,int b,function<bool(T)> &check){
    return find(a,b,check,0,0,n);
  }
  
};

//INSERT ABOVE HERE
signed main(){
  int n,l;
  scanf("%d %d",&n,&l);
  vector<int> v(n);
  for(int i=0;i<n;i++) scanf("%d",&v[i]);
  const int INF = 1e9+1;
  auto f=[](int a,int b){return min(a,b);};
  SegmentTree<int, int, decltype(f), decltype(f)> seg(n,f,f,INF);  
  seg.build(n,v);
  vector<int> ans(n-l+1);
  for(int i=0;i+l<=n;i++) ans[i]=seg.query(i,i+l);
  for(int i=0;i+l<=n;i++){
    if(i) printf(" ");
    printf("%d",ans[i]);
  }
  puts("");
  return 0;
}