【打CF，学算法——二星级】CodeForces 626C Block Towers（暴力/二分）

【CF简介】

提交链接：CF 626C

题面：

C. Block Towers

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

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.

Input

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.

Output

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

Examples

input

1 3

output

9

input

3 2

output

8

input

5 0

output

10

Note

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.

题意：

     两类学生，n个学生使用2块为单位的积木搭塔，m个学生使用3块为单位的积木搭塔，要求为每位学生分配一个互不相同的高度，且使得最高的高度最小。

解题：

    想到的是二分求解，结果看了别人居然用暴力直接过....，还是要仔细斟酌数据量啊！

代码：

#include <iostream>
#include <string>
#include <cstdio>
using namespace std;
int main()
{
	int a,b,tmp,g,ans,rep,va,vb;
    scanf("%d%d",&a,&b);
	   int le=1,ri=1000000000;
	   while(le<=ri)
	   {
		   int mid=(le+ri)>>1;
		   va=mid/2;
		   vb=mid/3;
		   rep=mid/6;
		   if(va>=a&&vb>=b&&va+vb-rep>=a+b)
		   {
			   ans=mid;
			   ri=mid-1;
		   }
		   else
			   le=mid+1;
	   }
	printf("%d\n",ans);
	return 0;
}