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;

class Program
{
    static string InputPattern = "InputX";

    static List<string> GetInputList()
    {
        var WillReturn = new List<string>();

        if (InputPattern == "Input1") {
            WillReturn.Add("1 6");
            //2
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("12345 678901");
            //175897
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static void Main()
    {
        List<string> InputList = GetInputList();
        long[] wkArr = InputList[0].Split(' ').Select(X => long.Parse(X)).ToArray();

        long N = wkArr[0];
        long M = wkArr[1];

        Console.WriteLine(ExecNibunHou(N, M));
    }

    //2分法で最大で何件のSccを作れるかを返す
    static long ExecNibunHou(long pS, long pC)
    {
        long L = 0;
        long R = pS + pC;

        while (L + 1 < R) {
            long Mid = (L + R) / 2;

            bool CanCreate = DeriveCanCreate(Mid, pS, pC);
            if (CanCreate) L = Mid;
            else R = Mid;
        }
        return L;
    }

    //K個のSccを作れるかを返す
    static bool DeriveCanCreate(long pK, long pS, long pC)
    {
        //Cを作成
        if (pK * 2 > pC)
            return false;
        pC -= pK * 2;

        //Sを作成
        if (pK > pS + pC / 2)
            return false;

        return true;
    }
}