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 .

输入描述:

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 ai and bi(0 ≤ ai, bi ≤ 105) — the characteristics of the i-th user.

输出描述:

Print (max bi) + 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.