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.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.Closeable;
import java.io.FileInputStream;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.HashMap;
import java.util.HashSet;
import java.util.TreeMap;

public class Main {
	static ContestScanner in;static Writer out;public static void main(String[] args)
	{try{in=new ContestScanner();out=new Writer();Main solve=new Main();solve.solve(in,out);
	in.close();out.close();}catch(IOException e){e.printStackTrace();}}
	void dump(int[]a){for(int i=0;i<a.length;i++)out.print(a[i]+" ");out.println();}
	void dump(int[]a,int n){for(int i=0;i<a.length;i++)out.printf("%"+n+"d",a[i]);out.println();}
	void dump(long[]a){for(int i=0;i<a.length;i++)out.print(a[i]+" ");out.println();}
	void dump(char[]a){for(int i=0;i<a.length;i++)out.print(a[i]);out.println();}
	long pow(long a,int n){long r=1;while(n>0){if((n&1)==1)r*=a;a*=a;n>>=1;}return r;}
	String itob(int a,int l){return String.format("%"+l+"s",Integer.toBinaryString(a)).replace(' ','0');}
	void sort(int[]a){m_sort(a,0,a.length,new int[a.length]);}
	void m_sort(int[]a,int s,int sz,int[]b)
	{if(sz<7){for(int i=s;i<s+sz;i++)for(int j=i;j>s&&a[j-1]>a[j];j--)swap(a, j, j-1);return;}
	m_sort(a,s,sz/2,b);m_sort(a,s+sz/2,sz-sz/2,b);int idx=s;int l=s,r=s+sz/2;final int le=s+sz/2,re=s+sz;
	while(l<le&&r<re){if(a[l]>a[r])b[idx++]=a[r++];else b[idx++]=a[l++];}
	while(r<re)b[idx++]=a[r++];while(l<le)b[idx++]=a[l++];for(int i=s;i<s+sz;i++)a[i]=b[i];
	} /* qsort(3.5s)<<msort(9.5s)<<<shuffle+qsort(17s)<Arrays.sort(Integer)(20s) */
	void swap(int[] a,int i,int j){final int t=a[i];a[i]=a[j];a[j]=t;}
	int binarySearchSmallerMax(int[]a,int v)// get maximum index which a[idx]<=v
	{int l=0,r=a.length-1,s=0;while(l<=r){int m=(l+r)/2;if(a[m]>v)r=m-1;else{l=m+1;s=m;}}return a[s]>v?-1:s;}
	void solve(ContestScanner in,Writer out) throws NumberFormatException, IOException{
		int a = in.nextInt();
		int b = in.nextInt();
		int h = 1;
		int maxSize = 0;
		int both = 0;
		while(a>0 || b>0){
			if(h%2==0 || h%3==0){
				if(h%2==0 && h%3==0){
					if(b<=0) a--;
					else{
						both++;
						b--;
					}
				}else if(h%3==0){
					if(b<=0 && both>0){
						both--;
						a--;
					}else if(b>0) b--;
				}else{
					a--;
				}
				maxSize = h;
			}
			h++;
		}
		System.out.println(maxSize);
	}
}

class MultiSet<T> extends HashMap<T, Integer>{
	@Override
	public Integer get(Object key){return containsKey(key)?super.get(key):0;}
	public void add(T key,int v){put(key,get(key)+v);}
	public void add(T key){put(key,get(key)+1);}
	public void sub(T key)
	{final int v=get(key);if(v==1)remove(key);else put(key,v-1);}
}
class OrderedMultiSet<T> extends TreeMap<T, Integer>{
	@Override
	public Integer get(Object key){return containsKey(key)?super.get(key):0;}
	public void add(T key,int v){put(key,get(key)+v);}
	public void add(T key){put(key,get(key)+1);}
	public void sub(T key)
	{final int v=get(key);if(v==1)remove(key);else put(key,v-1);}
}
class Pair implements Comparable<Pair>{
	int a,b;int hash;Pair(int a,int b){this.a=a;this.b=b;hash=(a<<16|a>>16)^b;}
	public boolean equals(Object obj){Pair o=(Pair)(obj);return a==o.a&&b==o.b;}
	public int hashCode(){return hash;}
	public int compareTo(Pair o){if(a!=o.a)return a<o.a?-1:1;else if(b!=o.b)return b<o.b?-1:1;return 0;}
}
class Timer{
	long time;
	public void set(){time=System.currentTimeMillis();}
	public long stop(){return time=System.currentTimeMillis()-time;}
	public void print()
	{System.out.println("Time: "+(System.currentTimeMillis()-time)+"ms");}
	@Override public String toString(){return"Time: "+time+"ms";}
}
class Writer extends PrintWriter{
	public Writer(String filename)throws IOException
	{super(new BufferedWriter(new FileWriter(filename)));}
	public Writer()throws IOException{super(System.out);}
}
class ContestScanner implements Closeable{
	private BufferedReader in;private int c=-2;
	public ContestScanner()throws IOException 
	{in=new BufferedReader(new InputStreamReader(System.in));}
	public ContestScanner(String filename)throws IOException
	{in=new BufferedReader(new InputStreamReader(new FileInputStream(filename)));}
	public String nextToken()throws IOException {
		StringBuilder sb=new StringBuilder();
		while((c=in.read())!=-1&&Character.isWhitespace(c));
		while(c!=-1&&!Character.isWhitespace(c)){sb.append((char)c);c=in.read();}
		return sb.toString();
	}
	public String readLine()throws IOException{
		StringBuilder sb=new StringBuilder();if(c==-2)c=in.read();
		while(c!=-1&&c!='\n'&&c!='\r'){sb.append((char)c);c=in.read();}
		return sb.toString();
	}
	public long nextLong()throws IOException,NumberFormatException
	{return Long.parseLong(nextToken());}
	public int nextInt()throws NumberFormatException,IOException
	{return(int)nextLong();}
	public double nextDouble()throws NumberFormatException,IOException 
	{return Double.parseDouble(nextToken());}
	public void close() throws IOException {in.close();}
}