Problem:
Score : 600 points

Problem Statement

Ringo Mart, a convenience store, sells apple juice.

On the opening day of Ringo Mart, there were A cans of juice in stock in the morning.
Snuke buys B cans of juice here every day in the daytime.
Then, the manager checks the number of cans of juice remaining in stock every night.
If there are C or less cans, D new cans will be added to the stock by the next morning.

Determine if Snuke can buy juice indefinitely, that is, there is always B or more cans of juice in stock when he attempts to buy them.
Nobody besides Snuke buy juice at this store.

Note that each test case in this problem consists of T queries.

Constraints

1 \leq T \leq 300

1 \leq A, B, C, D \leq 10^{18}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

T
A_1 B_1 C_1 D_1
A_2 B_2 C_2 D_2
:
A_T B_T C_T D_T

In the i-th query, A = A_i, B = B_i, C = C_i, D = D_i.

Output

Print T lines. The i-th line should contain Yes if Snuke can buy apple juice indefinitely in the i-th query; No otherwise.

Sample Input 1

14
9 7 5 9
9 7 6 9
14 10 7 12
14 10 8 12
14 10 9 12
14 10 7 11
14 10 8 11
14 10 9 11
9 10 5 10
10 10 5 10
11 10 5 10
16 10 5 10
1000000000000000000 17 14 999999999999999985
1000000000000000000 17 15 999999999999999985

Sample Output 1

No
Yes
No
Yes
Yes
No
No
Yes
No
Yes
Yes
No
No
Yes

In the first query, the number of cans of juice in stock changes as follows: (D represents daytime and N represents night.)

9
→D 2
→N 11
→D 4
→N 13
→D 6
→N 6
→D x

In the second query, the number of cans of juice in stock changes as follows:

9
→D 2
→N 11
→D 4
→N 13
→D 6
→N 15
→D 8
→N 8
→D 1
→N 10
→D 3
→N 12
→D 5
→N 14
→D 7
→N 7
→D 0
→N 9
→D 2
→N 11
→D …

and so on, thus Snuke can buy juice indefinitely.

Sample Input 2

24
1 2 3 4
1 2 4 3
1 3 2 4
1 3 4 2
1 4 2 3
1 4 3 2
2 1 3 4
2 1 4 3
2 3 1 4
2 3 4 1
2 4 1 3
2 4 3 1
3 1 2 4
3 1 4 2
3 2 1 4
3 2 4 1
3 4 1 2
3 4 2 1
4 1 2 3
4 1 3 2
4 2 1 3
4 2 3 1
4 3 1 2
4 3 2 1

Sample Output 2

No
No
No
No
No
No
Yes
Yes
No
No
No
No
Yes
Yes
Yes
No
No
No
Yes
Yes
Yes
No
No
No

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

using System;
using System.Collections.Generic;
using System.Globalization;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Net;
using static System.Console;
using static System.Math;
using System.Runtime.InteropServices.WindowsRuntime;
using System.Xml;
using static MyIO.Cin;

class Program
{
    static int N;
    static void Solve()
    {
        N = NI();
        for (int i = 0; i < N; i++)
        {
            long A = NL();
            long B = NL();
            long C = NL();
            long D = NL();
            if (A < B || D < B)
            {
                Console.WriteLine("No"); continue;
            }
            else if (C >= B)
            {
                Console.WriteLine("Yes"); continue;
            }
            //C < ? < B,D を満たす?を作れるなら死ぬ
            long g = Gcd(B, D);
            long a = A % g;
            //a + gpしか作れない
            //Cより大きく最初の数
            long upc = a + Ceil(C - a+1, g) * g;
            if (C < upc && upc < B && upc < D)
            {
                Console.WriteLine("No");
            }
            else
            {
                Console.WriteLine("Yes");
            }
        }
    }
    static int Gcd(int a, int b)
    {
        return b == 0 ? a : Gcd(b, a % b);
    }
    static long Gcd(long a, long b)
    {
        return b == 0 ? a : Gcd(b, a % b);
    }
    static int Ceil(int a, int b)
    {
        return (a + b - 1) / b;
    }
    static long Ceil(long a, long b)
    {
        return (a + b - 1) / b;
    }
    static void Main(string[] args)
    {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
        Solve();
        Console.Out.Flush();
    }

}


namespace MyIO
{
    using System;
    using System.Text;
    using System.Globalization;

    public static class Cin
    {
        public static string NextToken()
        {
            StringBuilder tokenChars = new StringBuilder();
            bool tokenFinished = false;
            bool skipWhiteSpaceMode = true;
            while (!tokenFinished)
            {
                int nextChar = Console.Read();
                if (nextChar == -1)
                {
                    tokenFinished = true;
                }
                else
                {
                    char ch = (char)nextChar;
                    if (char.IsWhiteSpace(ch))
                    {
                        if (!skipWhiteSpaceMode)
                        {
                            tokenFinished = true;
                            if (ch == '\r' && (Environment.NewLine == "\r\n"))
                            {
                                Console.Read();
                            }
                        }
                    }
                    else
                    {
                        skipWhiteSpaceMode = false;
                        tokenChars.Append(ch);
                    }
                }
            }

            string token = tokenChars.ToString();
            return token;
        }

        public static int NI()
        {
            string token = Cin.NextToken();
            return int.Parse(token);
        }
        public static long NL()
        {
            string token = Cin.NextToken();
            return long.Parse(token);
        }
        public static double ND(bool acceptAnyDecimalSeparator = true)
        {
            string token = Cin.NextToken();
            if (acceptAnyDecimalSeparator)
            {
                token = token.Replace(',', '.');
                double result = double.Parse(token, CultureInfo.InvariantCulture);
                return result;
            }
            else
            {
                double result = double.Parse(token);
                return result;
            }
        }
        public static decimal NextDecimal(bool acceptAnyDecimalSeparator = true)
        {
            string token = Cin.NextToken();
            if (acceptAnyDecimalSeparator)
            {
                token = token.Replace(',', '.');
                decimal result = decimal.Parse(token, CultureInfo.InvariantCulture);
                return result;
            }
            else
            {
                decimal result = decimal.Parse(token);
                return result;
            }
        }
        public static int[] NIA(int N)
        {
            int[] a = new int[N];
            for (int i = 0; i < N; i++)
                a[i] = NI();
            return a;
        }

    }
}