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.
import java.math.*;
import java.io.*;
import java.util.*;
public class C626C{
   public static long[] cAr, div;
   public static int N,M,K;
   public static int[] numCycle;
   public static Map<Integer,Set<Integer>> map;
   public static long MOD = 1000000007;
   public static void main(String[] args) throws IOException{
      InputReader in=new InputReader(new InputStreamReader(System.in));
      PrintWriter out=new PrintWriter(new BufferedOutputStream(System.out));
      int[] ar=in.nextIntAr();
      int N=ar[0];
      int M=ar[1];
      long height=0;
      while(N>M+1 && M>0){
         height+=6;
         N-=3;
         M-=1;
      }
      while(M>1 && N>1){
         height+=6;
         N-=2;
         M-=2;
      }
      if(M==0 || N>1)
         height+=(long)2*(long)N;
      else height+=(long)3*(long)M;
      System.out.println(height);
   }
   
   public static void setUpChoose(int t){
      cAr=new long[t+1];
      div=new long[t+1];
      cAr[0]=1;
      div[0]=1;
      
      for(int x=1;x<=t;x++){
         cAr[x]=(x*cAr[x-1])%(MOD);
         div[x]=pow(cAr[x],MOD-2);} 
   }
   
   public static long choose(int x,int y){
      long a=cAr[x+y];
      long b=div[x];
      long c=div[y];
      a=(a*b)%MOD;
      a=(a*c)%MOD;
      return a;
   } 
   
   public static long pow(long a,long b){
      if(b==1) 
         return a;
      long c=b/2;
      long temp=pow(a,c)%MOD;
      temp=(temp*temp)%MOD;
      if(b%2==1) temp=temp*a;
      return temp%MOD;
   }
}

class InputReader{
   private BufferedReader br;
   public InputReader(InputStreamReader in){
      br=new BufferedReader(in);
   }
   public int nextInt(){
      try{
         return Integer.parseInt(br.readLine());}
      catch(IOException e){throw new InputMismatchException();}
   }
   public int[] nextIntAr(){
      try{
         String[] s=br.readLine().split(" ");
         int[] ret=new int[s.length];
         for(int x=0;x<s.length;x++)
            ret[x]=Integer.parseInt(s[x]);
         return ret;}
         
      catch(IOException e){throw new InputMismatchException();}
   }
   
   public long nextLong(){
      try{
         return Long.parseLong(br.readLine());}
      catch(IOException e){throw new InputMismatchException();}
   }
   public long[] nextLongAr(){
      try{
         String[] s=br.readLine().split(" ");
         long[] ret=new long[s.length];
         for(int x=0;x<s.length;x++)
            ret[x]=Long.parseLong(s[x]);
         return ret;}
         
      catch(IOException e){throw new InputMismatchException();}
   }
   
   public String[] nextStringAr(){
      try{
         return br.readLine().split(" ");}
         
      catch(IOException e){throw new InputMismatchException();}
   }
   
   public String nextString(){
      try{
         return br.readLine();}
         
      catch(IOException e){throw new InputMismatchException();}
   }
}
   
class Pair implements Comparable<Pair>{
   long a;
   long b;
   
   public Pair(long ma, long mb){
      a = ma;
      b = mb;
   }
   
   public int compareTo(Pair o){
      if(a == o.a){
         if(b==o.b) 
            return 0;
         return b<o.b?-1:1;
      }
      return a<o.a?-1:1;
   }
}