CF626C.Block Towers

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.

一个班级的学生正在用积木搭建塔。每位学生通过将积木块沿长度方向堆叠，搭建一座（非零高度的）塔。其中有 $ n $ 名学生使用由两块组成的积木单元，另有 $ m $ 名学生使用由三块组成的积木单元。

学生们既不希望使用过多的积木块，又希望彼此的塔高度互不相同，因此任意两名学生的塔所含积木块总数不得相等。求所有学生中最高塔所需的最小高度。

The first line of the input contains two space-separated integers n and m (0 ≤ n, m ≤ 1 000 000, n + m > 0) — the number of students using two-block pieces and the number of students using three-block pieces, respectively.

输入的第一行包含两个以空格分隔的整数 $n$ 和 $m$（$0 ≤ n, m ≤ 1 000 000$，且 $n + m > 0$），分别表示使用两块积木的学生人数和使用三块积木的学生人数。

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

输出一个整数，表示最高塔的最小可能高度。

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.

在第一种情况下，使用两块积木的学生可以搭建一座高度为 4 的塔，而使用三块积木的学生可以分别搭建高度为 3、6 和 9 的塔。最高的塔高度为 9 块。

在第二种情况下，使用两块积木的学生可以搭建高度为 2、4 和 8 的塔，使用三块积木的学生可以搭建高度为 3 和 6 的塔，最高塔的高度为 8 块。