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;
#define rep(i,n) for(int i = 0; i < (int)n; i++)
using ll = long long;
const int INF = 1e9;

template <typename T, typename F>
class SegTree{
  int n; T uni; F f;
  vector<T> dat;
public:
  SegTree(int _n, F f, T uni) : f(f), uni(uni) {
    n = 1;
    while(n < _n) n *= 2;
    dat = vector<T>(2*n,uni);
  }
  void set(int k, const T x) {
    dat[k+n] = x;
  }
  void build() {
    for(int i = n-1; i >= 0; i--) {
      dat[i] = f(dat[2*i],dat[2*i+1]);
    }
  }
  void update(int k, T x) {
    k += n;
    dat[k] = x;
    while(k >>= 1){
      dat[k] = f(dat[2*k],dat[2*k+1]);
    }
  }
  T query(int a, int b) {
    T l = uni, r = uni;
    for(a += n, b += n; a < b; a >>= 1, b >>= 1) {
      if(a & 1) l = f(l,dat[a++]);
      if(b & 1) r = f(dat[--b],r);
    }
    return f(l,r);
  }
};

int main(){
  int n, l;
  cin >> n >> l;
  auto f = [](int a, int b){return min(a,b);};
  SegTree<int,decltype(f)> st(n,f,INF);
  rep(i,n) {
    int a;
    cin >> a;
    st.set(i,a);
  }
  st.build();
  rep(i,n-l+1) {
    cout << st.query(i,i+l);
    if(i < n-l) cout << " ";
    else cout << endl;
  }
  return 0;
}