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: Runtime Error)

namespace AtCoder.ARC.D069
{
    using System;
    using System.Collections.Generic;
    using System.Linq;
    using System.Numerics;
    using System.IO;

    using AtCoder.ARC.IO;

    public class Quest
    {
        public object Solve(Parser parser)
        {
            int n = parser.Integer();

            var s = parser.ScanLine();

            string r = "";
            if (Assume(s, 'S', 'S', out r))
            {
                return r;
            }

            if (Assume(s, 'W', 'S', out r))
            {
                return r;
            }

            if (Assume(s, 'S', 'W', out r))
            {
                return r;
            }

            if (Assume(s, 'W', 'W', out r))
            {
                return r;
            }

            return "-1";
        }

        bool Assume(string s, char c0, char c1, out string ans)
        {
            var n = s.Length;
            var ans1 = new char[n];

            for (int j = 0; j < n; j++)
            {
                ans1[j] = ' ';
            }

            ans1[0] = c0;
            ans1[1] = c1;

            for (int i = 0; i < n - 2; i++)
            {
                ans1[i + 2] = Ask(s[i + 1] == 'o', ans1[i], ans1[i + 1]);
            }

            ans = String.Join("", ans1).TrimEnd(new char[] { ' ' });

            return
                ans1[0] == Ask(s[n - 1] == 'o', ans1[n - 2], ans1[n - 1]) &&
                ans1[1] == Ask(s[0] == 'o', ans1[n - 1], ans1[0]);
        }

        private char Ask(bool matched, char left, char right)
        {
            if (left == right)
            {
                return matched ? 'S' : 'W';
            }
            return matched ? 'W' : 'S';
        }
    }

    static class Program
    {
        static void Main(string[] args)
        {
            var i = new Parser(Console.OpenStandardInput());
            var o = new Printer(Console.OpenStandardOutput());
            var got = new Quest().Solve(i);
            o.WriteLine(got);
            o.Flush();
        }
    }
}
namespace AtCoder.ARC.IO
{
    #region IO

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

    public class Parser
    {
        public Parser(Stream stream)
        {
            str = stream;
        }

        public readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof;

        public bool IsEndOfStream
        {
            get { return isEof; }
        }

        public IEnumerable<Parser> Take(int n)
        {
            return Enumerable.Range(1, n).Select(_ => this);
        }

        private byte read()
        {
            if (isEof) return 0;
            if (ptr < len) return buf[ptr++];
            ptr = 0;
            if ((len = str.Read(buf, 0, 1024)) > 0) return buf[ptr++];
            isEof = true;
            return 0;
        }

        public char Char()
        {
            byte b;
            do b = read(); while ((b < 33 || 126 < b) && !isEof);
            return (char)b;
        }

        public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                sb.Append(b);
            return sb.ToString();
        }

        public string ScanLine()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b != '\n'; b = (char)read())
                if (b == 0) break;
                else if (b != '\r') sb.Append(b);
            return sb.ToString();
        }

        public long Long()
        {
            if (isEof) return long.MinValue;
            long ret = 0;
            byte b;
            var ng = false;
            do b = read(); while (b != 0 && b != '-' && (b < '0' || '9' < b));
            if (b == 0) return long.MinValue;
            if (b == '-')
            {
                ng = true;
                b = read();
            }
            for (; ; b = read())
            {
                if (b < '0' || '9' < b)
                    return ng ? -ret : ret;
                ret = ret * 10 + b - '0';
            }
        }

        public int Integer()
        {
            return (isEof) ? int.MinValue : (int)Long();
        }

        public double Double()
        {
            var s = Scan();
            return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN;
        }

        static T[] enumerate<T>(int n, Func<T> f)
        {
            var a = new T[n];
            for (int i = 0; i < n; ++i) a[i] = f();
            return a;
        }

        public char[] Char(int n)
        {
            return enumerate(n, Char);
        }

        public string[] Scan(int n)
        {
            return enumerate(n, Scan);
        }

        public double[] Double(int n)
        {
            return enumerate(n, Double);
        }

        public int[] Integer(int n)
        {
            return enumerate(n, Integer);
        }

        public long[] Long(int n)
        {
            return enumerate(n, Long);
        }
    }

    public class Printer : StreamWriter
    {
        public override IFormatProvider FormatProvider
        {
            get { return CultureInfo.InvariantCulture; }
        }

        public Printer(Stream stream)
            : base(stream, new UTF8Encoding(false, true))
        {
        }

        public Printer(Stream stream, Encoding encoding)
            : base(stream, encoding)
        {
        }

        public void Write<T>(string format, T[] source)
        {
            base.Write(format, source.OfType<object>().ToArray());
        }

        public void WriteLine<T>(string format, T[] source)
        {
            base.WriteLine(format, source.OfType<object>().ToArray());
        }
    }

    #endregion

}