CF436F.Banners

All modern mobile applications are divided into free and paid. Even a single application developers often release two versions: a paid version without ads and a free version with ads.

Suppose that a paid version of the app costs p (p is an integer) rubles, and the free version of the application contains c ad banners. Each user can be described by two integers: a__i — the number of rubles this user is willing to pay for the paid version of the application, and b__i — the number of banners he is willing to tolerate in the free version.

The behavior of each member shall be considered strictly deterministic:

• if for user i, value b__i is at least c, then he uses the free version,
• otherwise, if value a__i is at least p, then he buys the paid version without advertising,
• otherwise the user simply does not use the application.

Each user of the free version brings the profit of c × w rubles. Each user of the paid version brings the profit of p rubles.

Your task is to help the application developers to select the optimal parameters p and c. Namely, knowing all the characteristics of users, for each value of c from 0 to (max b__i) + 1 you need to determine the maximum profit from the application and the corresponding parameter p.

所有现代移动应用程序都分为免费版和付费版。即使是单一应用程序，开发者也常常会发布两个版本：无广告的付费版和含广告的免费版。

假设该应用程序的付费版本售价为 $p$（$p$ 为整数）卢布，而免费版本中包含 $c$ 个广告横幅。每位用户可用两个整数描述：$a_i$ —— 该用户愿意为付费版本支付的卢布数；$b_i$ —— 该用户在免费版本中所能容忍的广告横幅数量。

每位用户的行为被严格视为确定性的：

• 若对用户 $i$，其 $b_i \ge c$，则他使用免费版本；
• 否则，若其 $a_i \ge p$，则他购买无广告的付费版本；
• 否则，该用户将完全不使用该应用程序。

每位免费版本用户带来的利润为 $c \times w$ 卢布；每位付费版本用户带来的利润为 $p$ 卢布。

你的任务是帮助应用程序开发者选择最优参数 $p$ 和 $c$。具体而言，在已知所有用户特征的前提下，对每个 $c$ 值（从 $0$ 到 $\max b_i + 1$），你需要确定应用程序所能获得的最大利润及对应的参数 $p$。

The first line contains two integers n and w (1 ≤ n ≤ 105; 1 ≤ w ≤ 105) — the number of users and the profit from a single banner. Each of the next n lines contains two integers a__i and b__i (0 ≤ a__i, b__i ≤ 105) — the characteristics of the i-th user.

第一行包含两个整数 $n$ 和 $w$（$1 ≤ n ≤ 10^5$；$1 ≤ w ≤ 10^5$）——分别表示用户数量和单个横幅带来的收益。接下来的 $n$ 行中，每行包含两个整数 $a_i$ 和 $b_i$（$0 ≤ a_i, b_i ≤ 10^5$）——表示第 $i$ 个用户的特征。

Print (max b__i) + 2 lines, in the i-th line print two integers: pay — the maximum gained profit at c = i - 1, p (0 ≤ p ≤ 109) — the corresponding optimal app cost. If there are multiple optimal solutions, print any of them.

输出 (_max_ _b__i_) + 2 行，在第 i 行输出两个整数：_pay_ —— 当 c = _i_ - 1 时所能获得的最大利润，_p_（0 ≤ _p_ ≤ 10^9）—— 对应的最优应用售价。若存在多个最优解，输出任意一个即可。