Problem:
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Sliding Minimum Element

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.

Sample Input 1

7 3
1 7 7 4 8 1 6

Sample Output 1

1 4 4 1 1

Solution in C++14 (judge verdict: Accepted)

#include <bits/stdc++.h>
 
using namespace std;
 
#define DEBUG(x) cerr<<#x<<": "<<x<<endl;
#define DEBUG_VEC(v) cerr<<#v<<":";for(int i=0;i<v.size();i++) cerr<<" "<<v[i]; cerr<<endl;
#define DEBUG_MAT(v) cerr<<#v<<endl;for(int i=0;i<v.size();i++){for(int j=0;j<v[i].size();j++) {cerr<<v[i][j]<<" ";}cerr<<endl;}
typedef long long ll;
//#define int ll
 
#define vi vector<int>
#define vl vector<ll>
#define vii vector< vector<int> >
#define vll vector< vector<ll> >
#define vs vector<string>
#define pii pair<int,int>
#define pis pair<int,string>
#define psi pair<string,int>
#define pll pair<ll,ll>
template<class S, class T> pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t) { return pair<S, T>(s.first + t.first, s.second + t.second); }
template<class S, class T> pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t) { return pair<S, T>(s.first - t.first, s.second - t.second); }
template<class S, class T> ostream& operator<<(ostream& os, pair<S, T> p) { os << "(" << p.first << ", " << p.second << ")"; return os; }
#define X first
#define Y second
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define rep1(i,n) for(int i=1;i<=(int)(n);i++)
#define rrep(i,n) for(int i=(int)(n)-1;i>=0;i--)
#define rrep1(i,n) for(int i=(int)(n);i>0;i--)
#define REP(i,a,b) for(int i=a;i<b;i++)
#define in(x, a, b) (a <= x && x < b)
#define all(c) c.begin(),c.end()
template<class T> bool chmax(T &a, const T &b) { if (a<b) { a = b; return 1; } return 0; }
template<class T> bool chmin(T &a, const T &b) { if (a>b) { a = b; return 1; } return 0; }
#define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end());
const ll inf = 1000000001;
const ll INF = (ll)1e18 + 1;
const long double pi = 3.1415926535897932384626433832795028841971L;
#define Sp(p) cout<<setprecision(25)<< fixed<<p<<endl;
//int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
//int dx2[8] = { 1,1,0,-1,-1,-1,0,1 }, dy2[8] = { 0,1,1,1,0,-1,-1,-1 };
vi dx = {1, 0, -1, 0}, dy = {0, 1, 0, -1};
vi dx2 = { 1,1,0,-1,-1,-1,0,1 }, dy2 = { 0,1,1,1,0,-1,-1,-1 };
#define fio() cin.tie(0); ios::sync_with_stdio(false);
const ll MOD = 1000000007;
//const ll MOD = 998244353;
// #define mp make_pair
//#define endl '\n'


ll ggcd(ll a, ll b) {
  if (b > a) {
    swap(a, b);
  }
  if (b == 0) return a;
  ll r = a%b;
  while (r != 0) {
    a = b;
    b = r;
    r = a%b;
  }
  return b;
}



template< typename Semigroup >
struct DisjointSparseTable {
  using F = function< Semigroup(Semigroup, Semigroup) >;
  const F f;
  vector< vector< Semigroup > > st;

  DisjointSparseTable(const vector< Semigroup > v, const F f) : f(f) {

    int b = 0;
    while((1 << b) <= v.size()) ++b;
    st.resize(b, vector< Semigroup >(v.size(), Semigroup()));
    for(int i = 0; i < v.size(); i++) st[0][i] = v[i];
    for(int i = 1; i < b; i++) {
      int shift = 1 << i;
      for(int j = 0; j < v.size(); j += shift << 1) {
        int t = min(j + shift, (int) v.size());
        st[i][t - 1] = v[t - 1];
        for(int k = t - 2; k >= j; k--) st[i][k] = f(v[k], st[i][k + 1]);
        if(v.size() <= t) break;
        st[i][t] = v[t];
        int r = min(t + shift, (int) v.size());
        for(int k = t + 1; k < r; k++) st[i][k] = f(st[i][k - 1], v[k]);
      }
    }
  }

  Semigroup query(int l, int r) {
    if(l >= --r) return st[0][l];
    int p = 31 - __builtin_clz(l ^ r);
    return f(st[p][l], st[p][r]);
  }
};

signed main() {
    fio();
    int n, l;
    cin >> n >> l;
    vl a(n);
    rep (i, n) {
        cin >> a[i];
    }

    auto f = [](int a, int b) {return min(a, b);};

    DisjointSparseTable<ll> spa(a, f);
    for (int i = 0; i + l <= n; i++) {
        cout << spa.query(i, i + l);
        if (i + l == n) cout << endl;
        else cout << " ";
    }
    // ll ans = 0;
    // rep (i, n) {
    //     if (a[i] == 1) {
    //         ans += n - i;
    //         continue;
    //     }
    //     if (spa.query(i, n) != 1) continue;
    //     int ng = n, ok = i + 1;
    //     while (ok + 1 < ng) {
    //         int mid = (ng + ok) / 2;
    //         if (spa.query(i, mid) == 1) ng = mid;
    //         else ok = mid;
    //     }
    //     ans += n + 1 - ng;
    // }
    // cout << ans << endl;
}