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>
#include <cmath>

using namespace std;
typedef long long ll;
//typedef unsigned long long ll;

#define rep(i, n) for (int i = 0; i < (n); ++i)
//#define rep(i, n) for (ll i = 0; i < (n); ++i)
//#define sz(x) ll(x.size())
//typedef pair<ll, int> P;
typedef pair<ll, ll> P;
//const double INF = 1e10;
const ll INF = LONG_LONG_MAX / 10;
//const ll INF = (1ll << 31) - 1;
//const ll INF = 1e15;
const ll MINF = LONG_LONG_MIN;
//const int INF = INT_MAX / 10;
#define cmin(x, y) x = min(x, y)
#define cmax(x, y) x = max(x, y)
//typedef pair<int, int> P;
//typedef pair<double, double> P;

bool contain(set<P> &s, P a) { return s.find(a) != s.end(); }

//ifstream myfile("C:\\Users\\riku\\Downloads\\0_00.txt");
//ofstream outfile("log.txt");
//outfile << setw(6) << setfill('0') << prefecture << setw(6) << setfill('0') << rank << endl;
// std::cout << std::bitset<8>(9);


void print_line(vector<ll> &line) {
    if (line.size() == 0ll) {
        cout << endl;
        return;
    }
    for (ll i = 0; i < line.size(); i++) {
        cout << line[i];
        if (i == line.size() - 1) cout << endl;
        else cout << ' ';
    }
}


typedef priority_queue<long long, vector<long long>, greater<long long>> PQ_ASK;
const int mod = 1000000007;

class CumulativeSum {
    vector<ll> numbers;
    vector<ll> sums;

public:
    CumulativeSum(int n) {
        numbers.resize(n);
        sums.resize(n);
    }

    void set(int i, ll value) {
        numbers[i] = value;
    }

    ll getSum(int i) {
        if (i == -1) return 0;
        if (i == sums.size()) return 0;
        return sums[i];
    }

    ll getSectionSum(int start, int end) {
        return getSum(end) - getSum(start - 1);
    }

    void calculate() {
        for (int i = 0; i < numbers.size(); i++) {
            sums[i] = getSum(i - 1) + numbers[i];
        }
    }

    ll upper_bound(ll query) {
        return distance(sums.begin(), std::upper_bound(sums.begin(), sums.end(), query));
    }

};


int main() {
    int n, q;

    cin >> n >> q;

    vector<ll> numbers(n);
    rep(i, n) cin >> numbers[i];

    set<ll> used;
    multiset<ll> used_m;

    vector<ll> ans;

    for (int r = 0; r < q; r++) {
        used.insert(numbers[r]);
        used_m.insert(numbers[r]);
    }
    ans.push_back(*used.begin());

    for (int k = 0; k + q < n; k++) {
        used.insert(numbers[k + q]);
        used_m.insert(numbers[k + q]);

        used_m.erase(used_m.find(numbers[k]));
        if (used_m.count(numbers[k]) == 0) {
            used.erase(numbers[k]);
        }
        ans.push_back(*used.begin());
    }
    print_line(ans);

}