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.*;
import static java.lang.Math.*;
import java.util.*;
import java.lang.*;

public class Main {
    final static boolean debug = false;
    final static String fileName = "";
    final static boolean useFiles = false;

    public static void main(String[] args) throws FileNotFoundException {
        PrintWriter writer = new PrintWriter(System.out);
        new Task(new InputReader(System.in), writer).solve();
        writer.close();
    }
}

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

    public byte nextByte() {
        return Byte.parseByte(next());
    }
}

class Task {
    boolean f(int n, int m, int x){
        int cnt2 = x / 2 - x / 6;
        int cnt3 = x / 3 - x / 6;
        n -= cnt2;
        if (n < 0) n = 0;
        m -= cnt3;
        if (m < 0) m = 0;

        int rest = n + m;
        return x / 6 >= rest;
    }

    public void solve() {
        int n = in.nextInt();
        int m = in.nextInt();

        int l = 1;
        int r = (int)1e9;
        while (r - l > 1){
            int mi = (l + r) / 2;
            if (f(n, m, mi)){
                r = mi;
            } else l = mi;
        }
        out.println(r);
    }

    private InputReader in;
    private PrintWriter out;

    Task(InputReader in, PrintWriter out) {
        this.in = in;
        this.out = out;
    }
}
