CF854B.Maxim Buys an Apartment

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题目描述

Maxim wants to buy an apartment in a new house at Line Avenue of Metropolis. The house has n apartments that are numbered from 1 to n and are arranged in a row. Two apartments are adjacent if their indices differ by 1. Some of the apartments can already be inhabited, others are available for sale.

Maxim often visits his neighbors, so apartment is good for him if it is available for sale and there is at least one already inhabited apartment adjacent to it. Maxim knows that there are exactly k already inhabited apartments, but he doesn't know their indices yet.

Find out what could be the minimum possible and the maximum possible number of apartments that are good for Maxim.

马克西姆想在大都会市线街的新楼里买一套公寓。这栋楼共有 nn 套公寓,编号从 11 到 nn,并排成一行。若两套公寓的编号之差为 11,则称它们相邻。其中一些公寓已被入住,其余则待售。

由于马克西姆经常拜访邻居,因此一套公寓对他而言是“合适的”,当且仅当它目前待售,且至少有一个已入住的相邻公寓。马克西姆知道目前已恰好有 kk 套公寓被入住,但他尚不清楚这些已入住公寓的具体编号。

请确定:对所有可能的已入住公寓分布方式,马克西姆“合适的”公寓数量的最小可能值与最大可能值分别是多少?

输入格式

The only line of the input contains two integers: n and k (1 ≤ n ≤ 109, 0 ≤ k ≤ n).

输入仅包含一行,有两个整数:nn 和 kk(1 ≤ n ≤ 1091 ≤ n ≤ 10^9,0 ≤ k ≤ n0 ≤ k ≤ n)。

输出格式

Print the minimum possible and the maximum possible number of apartments good for Maxim.

输出适合马克西姆的公寓的最少可能数量和最多可能数量。

输入输出样例

  • 输入#1

    6 3

    输出#1

    1 3

说明/提示

In the sample test, the number of good apartments could be minimum possible if, for example, apartments with indices 1, 2 and 3 were inhabited. In this case only apartment 4 is good. The maximum possible number could be, for example, if apartments with indices 1, 3 and 5 were inhabited. In this case all other apartments: 2, 4 and 6 are good.

在样例测试中,如果例如编号为 1、2 和 3 的公寓被占用,则好公寓的数量可达到最小值。此时仅有编号为 4 的公寓是好公寓。而好公寓数量的最大值可能出现在例如编号为 1、3 和 5 的公寓被占用的情况下。此时其余所有公寓:2、4 和 6 均为好公寓。

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