Vasya and Maximum Profit

#### 题目描述 有 $n$ 道题目，而我们可亲可敬的 $\tt Coin\; Collection\; Function$（下文简称 $\tt FCC$）正以极高的热情筹备着比赛！ 如果 $\tt FCC$ 将第 $i$ 道题作为比赛题，$\tt FCC$ 需要支付 $c_i$ 元给工作人员。但是 $\tt FCC$ 每增加一道题，就可以获得 $a$ 元的“自愿捐助”款。 现在 $\tt FCC$ 想选择一个连续区间 $[l,r]$ 作为比赛题。 题目的难度需要相差不大，否则容易引起选手憎恨。每个题目有一个难度 $d_i$ ，$\tt FCC$ 会额外支付 $\max_{i=l}^{r-1}(d_{i+1}-d_{i})^2$ 元来堵住媒体的嘴。特别的，若 $l=r$ 则无这一笔额外款项。 $\tt FCC$ 精打细算，想要获得最多的钱。请你告诉 $\tt FCC$ ，最多能赚多少钱吧！ #### 输入格式 第一行是 $n,a$ ，含义如题。 接下来 $n$ 行，第 $i+1$ 行是两个数 $d_i,c_i$ ，描述一道题。变量含义如题。 #### 输出格式 仅一行一个整数。需要输出的值见题面。 #### 数据范围与提示 $1\le n\le 3\times 10^5$ 且 $1\le a\le 10^9$ 且 $1\le d_i<d_{i+1}\le 10^9$ 且 $1\le c_i\le 10^9$ 。

Vasya got really tired of these credits (from problem F) and now wants to earn the money himself! He decided to make a contest to gain a profit. Vasya has $ n $ problems to choose from. They are numbered from $ 1 $ to $ n $ . The difficulty of the $ i $ -th problem is $ d_i $ . Moreover, the problems are given in the increasing order by their difficulties. The difficulties of all tasks are pairwise distinct. In order to add the $ i $ -th problem to the contest you need to pay $ c_i $ burles to its author. For each problem in the contest Vasya gets $ a $ burles. In order to create a contest he needs to choose a consecutive subsegment of tasks. So the total earnings for the contest are calculated as follows: - if Vasya takes problem $ i $ to the contest, he needs to pay $ c_i $ to its author; - for each problem in the contest Vasya gets $ a $ burles; - let $ gap(l, r) = \max\limits_{l \le i < r} (d_{i + 1} - d_i)^2 $ . If Vasya takes all the tasks with indices from $ l $ to $ r $ to the contest, he also needs to pay $ gap(l, r) $ . If $ l = r $ then $ gap(l, r) = 0 $ . Calculate the maximum profit that Vasya can earn by taking a consecutive segment of tasks.

The first line contains two integers $ n $ and $ a $ ( $ 1 \le n \le 3 \cdot 10^5 $ , $ 1 \le a \le 10^9 $ ) — the number of proposed tasks and the profit for a single problem, respectively. Each of the next $ n $ lines contains two integers $ d_i $ and $ c_i $ ( $ 1 \le d_i, c_i \le 10^9, d_i < d_{i+1} $ ).

Print one integer — maximum amount of burles Vasya can earn.

5 10
1 15
5 3
6 11
7 2
11 22

13

3 5
1 8
2 19
3 11

0