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*.
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.
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.
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