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;

////////////////////////////////////////////////////////////////////////////////////////////

template<typename T, typename Monoid>
struct SlidingWindowAggregation {
    T unity;
    Monoid merge;
    vector<pair<T, T>> front, back;

    SlidingWindowAggregation(Monoid f, T id) : merge(f), unity(id) {}

    bool empty() const {return front.empty() and back.empty();}

    int size() const {return front.size() + back.size();}

    T fold_all() const {
        T vf = front.empty() ? unity : front.back().second;
        T vb = back.empty() ? unity : back.back().second;
        return merge(vf,vb);
    }

    void emplace(const T &val) {
        if (back.empty()) {
            back.emplace_back(val,val);
        } else {
            back.emplace_back(val,merge(back.back().second,val));
        }
    }

    void pop() {
        assert(!empty());
        if (front.empty()) {
            front.emplace_back(back.back().first,back.back().first);
            back.pop_back();
            while (!back.empty()) {
                front.emplace_back(back.back().first,merge(back.back().first,front.back().second));
                back.pop_back();
            }
        }
        front.pop_back();
    }
};

///////////////////////////////////////////////////////////////////////////////////////////

void DSL_3_D() {
    int N,L; cin >> N >> L;
    vector<int> A(N);
    for (int i = 0; i < N; i++) cin >> A[i];

    auto f=[](int a, int b) {return min(a,b);};
    const int id = 1e9;
    SlidingWindowAggregation<int, decltype(f)> SWAG(f,id);
    vector<int> ans;
    for (int i = 0; i < N; i++) {
        if (i < L) {
            SWAG.emplace(A[i]);
        } else {
            ans.emplace_back(SWAG.fold_all());
            SWAG.emplace(A[i]);
            SWAG.pop();
        }
    }
    ans.emplace_back(SWAG.fold_all());
    for (int i = 0; i < ans.size(); i++) {
        if (i) cout << " ";
        cout << ans[i];
    }
    cout << endl;
}

int main() {
    ios::sync_with_stdio(false); cin.tie(nullptr);
    DSL_3_D();
}

/*
  verified on 2020/06/07
  http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DSL_3_D&lang=ja
*/