Problem:
Score : 400 points

Problem Statement

There are N squares in a row.
The leftmost square contains the integer A, and the rightmost contains the integer B. The other squares are empty.

Aohashi would like to fill the empty squares with integers so that the following condition is satisfied:

For any two adjacent squares, the (absolute) difference of the two integers in those squares is between C and D (inclusive).

As long as the condition is satisfied, it is allowed to use arbitrarily large or small integers to fill the squares.
Determine whether it is possible to fill the squares under the condition.

Constraints

3 \leq N \leq 500000

0 \leq A \leq 10^9

0 \leq B \leq 10^9

0 \leq C \leq D \leq 10^9

All input values are integers.

Input

Input is given from Standard Input in the following format:

N A B C D

Output

Print YES if it is possible to fill the squares under the condition; print NO otherwise.

Sample Input 1

5 1 5 2 4

Sample Output 1

YES

For example, fill the squares with the following integers: 1, -1, 3, 7, 5, from left to right.

Sample Input 2

4 7 6 4 5

Sample Output 2

NO

Sample Input 3

48792 105960835 681218449 90629745 90632170

Sample Output 3

NO

Sample Input 4

491995 412925347 825318103 59999126 59999339

Sample Output 4

YES

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

using Training20200609.Questions;
using Training20200609.Extensions;
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;

namespace Training20200609.Questions
{
    /// <summary>
    /// https://atcoder.jp/contests/agc017/tasks/agc017_b
    /// </summary>
    public class QuestionD : AtCoderQuestionBase
    {
        public override IEnumerable<object> Solve(TextReader inputStream)
        {
            var nabcd = inputStream.ReadLongArray();
            var n = nabcd[0] - 1;
            var diff = Math.Abs(nabcd[1] - nabcd[2]);
            var c = nabcd[3];
            var d = nabcd[4];
            var midDoubled = c + d;
            var width = d - c;

            if (n % 2 == 0)
            {
                for (int i = 0; i * 2 <= n; i++)
                {
                    var small = midDoubled * i - width * n / 2;
                    var large = midDoubled * i + width * n / 2;

                    if (small <= diff && diff <= large)
                    {
                        yield return "YES";
                        yield break;
                    }
                }
            }
            else
            {
                var targetSmall = new long[] { -diff + c, diff + c };
                var targetLarge = new long[] { -diff + d, diff + d };

                for (int i = 0; i * 2 <= n; i++)
                {
                    var small = midDoubled * i - width * (n - 1) / 2;
                    var large = midDoubled * i + width * (n - 1) / 2;

                    for (int j = 0; j < 2; j++)
                    {
                        if ((targetSmall[j] <= small && small <= targetLarge[j]) || (targetSmall[j] <= large && large <= targetLarge[j]) || 
                            (small <= targetSmall[j] && targetSmall[j] <= large))
                        {
                            yield return "YES";
                            yield break;
                        }
                    }
                }
            }

            yield return "NO";
        }


    }
}


namespace Training20200609
{
    class Program
    {
        static void Main(string[] args)
        {
            IAtCoderQuestion question = new QuestionD();    // 問題に合わせて書き換え
            var answers = question.Solve(Console.In);
            foreach (var answer in answers)
            {
                Console.WriteLine(answer);
            }
        }
    }
}

#region Base Classes

namespace Training20200609.Questions
{

    public interface IAtCoderQuestion
    {
        IEnumerable<object> Solve(string input);
        IEnumerable<object> Solve(TextReader inputStream);
    }

    public abstract class AtCoderQuestionBase : IAtCoderQuestion
    {
        public IEnumerable<object> Solve(string input)
        {
            var stream = new MemoryStream(Encoding.Unicode.GetBytes(input));
            var reader = new StreamReader(stream, Encoding.Unicode);

            return Solve(reader);
        }

        public abstract IEnumerable<object> Solve(TextReader inputStream);
    }

}

#endregion

#region Extensions

namespace Training20200609.Extensions
{
    internal static class TextReaderExtensions
    {
        internal static int ReadInt(this TextReader reader) => int.Parse(ReadString(reader));
        internal static long ReadLong(this TextReader reader) => long.Parse(ReadString(reader));
        internal static double ReadDouble(this TextReader reader) => double.Parse(ReadString(reader));
        internal static string ReadString(this TextReader reader) => reader.ReadLine();

        internal static int[] ReadIntArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(int.Parse).ToArray();
        internal static long[] ReadLongArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(long.Parse).ToArray();
        internal static double[] ReadDoubleArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(double.Parse).ToArray();
        internal static string[] ReadStringArray(this TextReader reader, char separator = ' ') => reader.ReadLine().Split(separator);
    }
}

#endregion