Block Towers

题意翻译

一群人在搭建积木塔。 有N个人2块2块往上搭，有M个人3块3块往上搭，每个人塔的高度都要大于0，且高度各不相同，问最高的塔高度的最小值。(0<=n,m<=1000000)

题目描述

Students in a class are making towers of blocks. Each student makes a (non-zero) tower by stacking pieces lengthwise on top of each other. $ n $ of the students use pieces made of two blocks and $ m $ of the students use pieces made of three blocks. The students don’t want to use too many blocks, but they also want to be unique, so no two students’ towers may contain the same number of blocks. Find the minimum height necessary for the tallest of the students' towers.

输入输出格式

输入格式

The first line of the input contains two space-separated integers $ n $ and $ m $ ( $ 0<=n,m<=1000000 $ , $ n+m&gt;0 $ ) — the number of students using two-block pieces and the number of students using three-block pieces, respectively.

输出格式

Print a single integer, denoting the minimum possible height of the tallest tower.

输入输出样例

输入样例 #1

1 3

输出样例 #1

9

输入样例 #2

3 2

输出样例 #2

8

输入样例 #3

5 0

输出样例 #3

10

说明

In the first case, the student using two-block pieces can make a tower of height $ 4 $ , and the students using three-block pieces can make towers of height $ 3 $ , $ 6 $ , and $ 9 $ blocks. The tallest tower has a height of $ 9 $ blocks. In the second case, the students can make towers of heights $ 2 $ , $ 4 $ , and $ 8 $ with two-block pieces and towers of heights $ 3 $ and $ 6 $ with three-block pieces, for a maximum height of $ 8 $ blocks.