16188번 - Histogram Sequence 다국어

문제

A histogram is a polygon made by aligning $N$ adjacent rectangles that share a common base line. Each rectangle is called a bar. The $i$-th bar from the left has width 1 and height $H_i$.

Figure: This picture depicts a case when $N = 9$ and $H = [7,\ 4,\ 3,\ 5,\ 4,\ 2,\ 5,\ 1,\ 2]$.

One day, you wanted to find the area of the largest rectangle contained in the given histogram. What you did was to make a list of integers $A$ by the following procedure:

• For each 1ドル \le i \le j \le N,ドル calculate the largest area of the rectangle contained in the histogram, where the rectangle's base line coincides with the base line of the $i,\ i+1,\ \cdots,\ j-1,\ j$-th bar. Add the area to the list $A$.

Figure: This picture depicts a case when $i = 3$ and $j = 5$. The area is 9.

The length of the list $A$ is exactly $\frac{N(N+1)}{2}$ since you chose each pair $(i,\ j)$ exactly once. To make your life easier, you sorted the list $A$ in non-decreasing order. Now, to find the largest area of the rectangle contained in the histogram, you just need to read the last element of $A,ドル $A_{N(N+1)/2}$.

However, you are not satisfied with this at all, so I decided to let you compute some part of the list $A$. You have to write a program that, given two indices $L$ and $R$ ($L \le R$), calculate the values $A_{L\cdots R},ドル i.e. $A_{L},\ A_{L+1},\ \cdots,\ A_{R-1},\ A_{R}$.

입력

The first line of the input contains an integer $N$ (1ドル \le N \le 300,000$) which is the number of bars in the histogram.

The next line contains $N$ space-separated positive integers $H_1,\ H_2,\ \cdots,\ H_N$ (1ドル \le H_i \le 10^9$), where $H_i$ is the height of the $i$-th bar.

The last line contains two integers $L$ and $R$ (1ドル \le L \le R \le \frac{N(N+1)}{2},ドル $R - L + 1 \le 300,000$).

출력

Print $R - L + 1$ integers. The $j$-th (1ドル \le j \le R-L+1$) of them should be the $(L+j-1)$-th element of the list $A,ドル i.e. $A_{L+j-1}$.

제한

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