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:
#define _USE_MATH_DEFINES
#define _CRT_SECURE_NO_WARNINGS

#include <iostream>
#include <string>
#include <sstream>
#include <iomanip>
#include <cmath>
#include <cstring>
#include <cstdlib>
#include <algorithm>
#include <stack>
#include <queue>
#include <vector>
#include <list>
#include <set>
#include <map>
#include <bitset>
#include <utility>
#include <numeric>

using namespace std;

using ll = long long;
using ull = unsigned long long;

const ll inf = (ll)1e9;
const ll mod = (ll)1e9 + 7;

int main()
{
	int n, k;
	cin >> n >> k;

	vector<int> a(n);
	for (int i = 0; i < n; i++)
	{
		cin >> a.at(i);
	}

	map<int, int> m;

	int r = 0;
	bool f = true;
	int minv = inf;
	for (int l = 0; l < n; l++)
	{
		while (r < n && r - l < k)
		{
			m[a.at(r)] ++;
			r++;
		}

		if (r - l == k)
		{
			map<int, int>::iterator iter = begin(m);
			pair<int, int> p = *iter;

			minv = min(minv, p.first);
			cout << (f ? "" : " ") << minv;

			minv = inf;
			f = false;
		}

		if (l == r)
		{
			r++;
		}
		else
		{
			m[a.at(l)] --;
			if (m[a.at(l)] == 0)
			{
				m.erase(a.at(l));
			}
		}
	}
	cout << endl;
}