Problem:
Score : 300 points

Problem Statement

Snuke loves puzzles.

Today, he is working on a puzzle using S- and c-shaped pieces.
In this puzzle, you can combine two c-shaped pieces into one S-shaped piece, as shown in the figure below:

Snuke decided to create as many Scc groups as possible by putting together one S-shaped piece and two c-shaped pieces.

Find the maximum number of Scc groups that can be created when Snuke has N S-shaped pieces and M c-shaped pieces.

Constraints

1 ≤ N,M ≤ 10^{12}

Input

The input is given from Standard Input in the following format:

N M

Output

Print the answer.

Sample Input 1

1 6

Sample Output 1

2

Two Scc groups can be created as follows:

Combine two c-shaped pieces into one S-shaped piece

Create two Scc groups, each from one S-shaped piece and two c-shaped pieces

Sample Input 2

12345 678901

Sample Output 2

175897

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace ProgrammingContest_CSharp
{
    class Program
    {
        static void Main(string[] args)
        {
            var e = Console.ReadLine().Split().Select(long.Parse).ToArray();
            long n = e[0], m = e[1];
            long ans = Solve(n, m);
            Console.WriteLine(ans);
        }

        private static long Solve(long n, long m)
        {
            long begin = 0, end = n + m;

            while (begin < end)
            {
                //Console.WriteLine($"{begin} {end}");
                long middle = (begin + end) / 2 + 1;

                if (CanCreate(middle, n, m))
                {
                    begin = middle;
                }
                else
                {
                    end = middle - 1;
                }
            }

            return begin;
        }

        private static bool CanCreate(long count, long n, long m)
        {
            long lack = Math.Max(count - n, 0);
            return m - lack * 2 >= count * 2;
        }
    }
}