Problem:
Score : 100 points

Problem Statement

Snuke is giving cookies to his three goats.

He has two cookie tins. One contains A cookies, and the other contains B cookies. He can thus give A cookies, B cookies or A+B cookies to his goats (he cannot open the tins).

Your task is to determine whether Snuke can give cookies to his three goats so that each of them can have the same number of cookies.

Constraints

1 \leq A,B \leq 100

Both A and B are integers.

Input

Input is given from Standard Input in the following format:

A B

Output

If it is possible to give cookies so that each of the three goats can have the same number of cookies, print Possible; otherwise, print Impossible.

Sample Input 1

4 5

Sample Output 1

Possible

If Snuke gives nine cookies, each of the three goats can have three cookies.

Sample Input 2

1 1

Sample Output 2

Impossible

Since there are only two cookies, the three goats cannot have the same number of cookies no matter what Snuke gives to them.

Solution in C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Xml.Schema;

namespace AtCoder
{
    public class Solver
    {
        private readonly IInputReader _inputReader;
        private readonly IOutputWriter _outputWriter;

        public Solver(IInputReader inputReader, IOutputWriter outputWriter)
        {
            _inputReader = inputReader;
            _outputWriter = outputWriter;
        }

        public void Solve()
        {
            var inputs = _inputReader.ReadLine().ToIntArray();

            var A = inputs[0];
            var B = inputs[1];
            var list = new List<int>() {A, B, A + B};
            var possible = list.Any(n => n >= 3 && n % 3 == 0);
            _outputWriter.WriteLine(possible ? "Possible" : "Impossible");
        }
    }

    public static class Combination
    {
        public static IEnumerable<T[]> Enumerate<T>(IEnumerable<T> items, int k, bool withRepetition)
        {
            if (k == 1)
            {
                foreach (var item in items)
                    yield return new T[] {item};
                yield break;
            }

            foreach (var item in items)
            {
                var leftside = new T[] {item};

                // item よりも前のものを除く （順列と組み合わせの違い)
                // 重複を許さないので、unusedから item そのものも取り除く
                var unused = withRepetition ? items : items.SkipWhile(e => !e.Equals(item)).Skip(1).ToList();

                foreach (var rightside in Enumerate(unused, k - 1, withRepetition))
                {
                    yield return leftside.Concat(rightside).ToArray();
                }
            }
        }
    }

    internal class Program
    {
        static void Main(string[] args)
        {
            var reader = new ConsoleInputReader();
            var writer = new ConsoleOutputWriter();
            new Solver(reader, writer).Solve();
        }
    }

    public interface IInputReader
    {
        string ReadLine();
    }

    public interface IOutputWriter
    {
        void WriteLine(string output);
    }

    internal class ConsoleInputReader : IInputReader
    {
        public string ReadLine() => Console.ReadLine();
    }

    internal class ConsoleOutputWriter : IOutputWriter
    {
        public void WriteLine(string output) => Console.WriteLine(output);
    }

    public static class StringExtensions
    {
        public static char ToChar(this string text) => text[0];
        public static string[] ToStringArray(this string text) => text.Split(' ').ToArray();
        public static int ToInt(this string text) => int.Parse(text);
        public static int[] ToIntArray(this string text) => text.Split(' ').Select(txt => txt.ToInt()).ToArray();
        public static long ToLong(this string text) => long.Parse(text);
        public static long[] ToLongArray(this string text) => text.Split(' ').Select(txt => txt.ToLong()).ToArray();

        public static string ToJoinedString(this string[] texts, string separator = "") =>
            string.Join(separator, texts);

        public static string ToJoinedString(this char[] chars) => string.Join("", chars);
        public static string ToYESNO(this bool b) => b ? "YES" : "NO";
        public static string ToYesNo(this bool b) => b ? "Yes" : "No";
    }

    public struct ModLong : IEquatable<ModLong>
    {
        private const long Mod = 1000000007;
        private readonly long _value;

        public ModLong(long value)
        {
            _value = (value % Mod + Mod) % Mod;
        }

        public bool Equals(ModLong other)
        {
            return _value == other._value;
        }

        public override bool Equals(object obj)
        {
            return obj is ModLong other && Equals(other);
        }

        public override int GetHashCode()
        {
            return _value.GetHashCode();
        }

        public static bool operator ==(ModLong left, ModLong right)
        {
            return left.Equals(right);
        }

        public static bool operator !=(ModLong left, ModLong right)
        {
            return !left.Equals(right);
        }

        public static ModLong operator +(ModLong left, ModLong right)
        {
            return (ModLong) (left._value + right._value);
        }

        public static ModLong operator -(ModLong left, ModLong right)
        {
            return (ModLong) (left._value - right._value);
        }

        public static ModLong operator *(ModLong left, ModLong right)
        {
            return (ModLong) (left._value * right._value);
        }

        public static ModLong operator /(ModLong left, ModLong right)
        {
            return (ModLong) (left._value * Util.ModInv(right._value, Mod));
        }

        public static explicit operator long(ModLong num)
        {
            return num._value;
        }

        public static explicit operator ModLong(long num)
        {
            return new ModLong(num);
        }

        public override string ToString() => _value.ToString();
    }

    public class ModCombination
    {
        private const int Max = 510000;
        private const long Mod = 1000000007;

        private long[] fac = new long[Max];
        private long[] finv = new long[Max];
        private long[] inv = new long[Max];

        public ModCombination()
        {
            fac[0] = 1;
            fac[1] = 1;
            finv[0] = 1;
            finv[1] = 1;
            inv[1] = 1;
            for (var i = 2; i < Max; i++)
            {
                fac[i] = fac[i - 1] * i % Mod;
                inv[i] = Mod - inv[Mod % i] * (Mod / i) % Mod;
                finv[i] = finv[i - 1] * inv[i] % Mod;
            }
        }

        /// <summary>
        /// mCn 組み合わせ
        /// </summary>
        /// <param name="m"></param>
        /// <param name="n"></param>
        /// <returns></returns>
        public long Combination(long m, long n)
        {
            if (m < n) return 0;
            if (m < 0 || n < 0) return 0;
            return fac[m] * (finv[n] * finv[m - n] % Mod) % Mod;
        }
    }

    public class Util
    {
        /// <summary>
        /// a^n mod を計算する
        /// </summary>
        /// <param name="a"></param>
        /// <param name="n"></param>
        /// <param name="mod"></param>
        /// <returns></returns>
        public static long ModPow(long a, long n, long mod)
        {
            long res = 1;
            while (n > 0)
            {
                if ((n & 1) == 1)
                {
                    res = res * a % mod;
                }

                a = a * a % mod;
                n >>= 1;
            }

            return res;
        }

        /// <summary>
        /// a^{-1} mod を計算する
        /// </summary>
        /// <param name="a"></param>
        /// <param name="mod"></param>
        /// <returns></returns>
        public static long ModInv(long a, long mod)
        {
            return ModPow(a, mod - 2, mod);
        }

        /// <summary>
        /// 階乗
        /// </summary>
        /// <param name="n"></param>
        /// <returns></returns>
        /// <exception cref="ArgumentOutOfRangeException"></exception>
        public static long ModFactional(long n)
        {
            if (n < 0) throw new ArgumentOutOfRangeException(nameof(n));
            ModLong result = (ModLong) 1;
            for (var i = 1; i <= n; i++)
            {
                result *= (ModLong) i;
            }

            return (long) result;
        }
    }
}