Description

An array of size n ≤ 10 ⁶ is given to you. There is a sliding window of size k which is moving from the very left of the array to the very right. You can only see the k numbers in the window. Each time the sliding window moves rightwards by one position. Following is an example: 
The array is [1 3 -1 -3 5 3 6 7], and k is 3.

Window position	Minimum value	Maximum value
[1  3  -1] -3  5  3  6  7	-1	3
1 [3  -1  -3] 5  3  6  7	-3	3
1  3 [-1  -3  5] 3  6  7	-3	5
1  3  -1 [-3  5  3] 6  7	-3	5
1  3  -1  -3 [5  3  6] 7	3	6
1  3  -1  -3  5 [3  6  7]	3	7

Your task is to determine the maximum and minimum values in the sliding window at each position. 

Input

The input consists of two lines. The first line contains two integers n and k which are the lengths of the array and the sliding window. There are n integers in the second line. 

Output

There are two lines in the output. The first line gives the minimum values in the window at each position, from left to right, respectively. The second line gives the maximum values. 

Sample Input

8 3
1 3 -1 -3 5 3 6 7

Sample Output

-1 -3 -3 -3 3 3
3 3 5 5 6 7

線段樹雖然可以水過，但複雜度比較高，可以用更優的單調佇列方法。

#include <iostream>
#include <cstdio>
using namespace std;

const int N = 1000005;

struct Elem
{
	int val;
	int pos;
};

Elem maxque[N];
Elem minque[N];
int maxhead, minhead, maxtail, mintail;
int maxans[N];
int minans[N];
int cur;

int main()
{
	int n, w, num;
	scanf("%d%d", &n, &w);
	minhead = mintail = 0;
	maxhead = maxtail = 0;
	cur = 0;
	for (int i = 0; i < w; ++i)
	{
		scanf("%d", &num);
		
		while (minhead < mintail && minque[mintail - 1].val >= num) --mintail;
		minque[mintail].val = num;
		minque[mintail].pos = i;
		++mintail;

		while (maxhead < maxtail && maxque[maxtail - 1].val <= num) --maxtail;
		maxque[maxtail].val = num;
		maxque[maxtail].pos = i;
		++maxtail;
	}
	for (int i = w; i < n; ++i)
	{
		minans[cur] = minque[minhead].val;
		maxans[cur] = maxque[maxhead].val;
		++cur;

		scanf("%d", &num);

		while (minhead < mintail && i - minque[minhead].pos >= w) ++minhead;
		while (minhead < mintail && minque[mintail - 1].val >= num) --mintail;
		minque[mintail].val = num;
		minque[mintail].pos = i;
		++mintail;
		
		while (maxhead < maxtail && i - maxque[maxhead].pos >= w) ++maxhead;
		while (maxhead < maxtail && maxque[maxtail - 1].val <= num) --maxtail;
		maxque[maxtail].val = num;
		maxque[maxtail].pos = i;
		++maxtail;
	}
	minans[cur] = minque[minhead].val;
	maxans[cur] = maxque[maxhead].val;
	++cur;
	
	for (int i = 0; i < cur; ++i)
	{
		if (i > 0) putchar(' ');
		printf("%d", minans[i]);
	}
	printf("\n");
	for (int i = 0; i < cur; ++i)
	{
		if (i > 0) putchar(' ');
		printf("%d", maxans[i]);
	}
	printf("\n");

	return 0;
}