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: Wrong Answer)

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

namespace ConsoleApplication1
{
    internal static class Program
    {
        public static void Main(string[] args)
        {
            Solve(Console.OpenStandardInput(), Console.OpenStandardOutput());
        }

        internal static void Solve(Stream inputStream, Stream outputStream)
        {
            // AGC 026 B - rng_10s
            var scanner = new StreamScanner(inputStream);
            var writer = new StreamWriter(outputStream)
            {
                AutoFlush = false
            };
            
            Action<string> Write = (string str) => writer.Write(str);
            Action<string> WriteLine = (string str) => writer.WriteLine(str);
            Action Flush = () => writer.Flush();

            var t = scanner.Integer();
         
            for (var i = 0; i < t; i++)
            {
                var a = scanner.Long();
                var b = scanner.Long();
                var c = scanner.Long();
                var d = scanner.Long();

                if (a < b || b > d)
                {
                    WriteLine("No");
                    continue;
                }

                var gcd = Gcd(b, d);
                var rem = a % gcd;
                var min = (c - rem) / gcd * gcd + gcd + rem;
                if (b > min)
                {
                    WriteLine("No");
                    continue;
                }
                WriteLine("Yes");    
            }
            Flush();
        }
        
        static long Gcd(long a, long b)
        {
            if (a < b) return Gcd(b, a);
            while(b != 0)
            {
                var r = a % b;
                a = b;
                b = r;
            }
            return a;
        }
        static int Gcd(int a, int b)
        {
            if (a < b) return Gcd(b, a);
            while(b != 0)
            {
                var r = a % b;
                a = b;
                b = r;
            }
            return a;
        }
    }
    
    // https://qiita.com/Camypaper/items/de6d576fe5513743a50e
    public class StreamScanner
    {   
        private readonly Stream stream;
        private readonly byte[] buf = new byte[1024];
        private int len, pos;
        private bool isEof = false;
        public bool IsEndOfStream => isEof;

        public StreamScanner(Stream stream) { this.stream = stream; }
        
        private byte Read()
        {
            if (isEof) throw new EndOfStreamException();
            if (pos >= len) {
                pos = 0;
                if ((len = stream.Read(buf, 0, 1024)) <= 0)
                {
                    isEof = true;
                    return 0;
                }
            }
            return buf[pos++];
        }
        
        public char Char() 
        {
            byte b = 0;
            do b = Read();
            while (b < 33 || 126 < b);
            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 long Long()
        {
            long ret = 0; byte b = 0; var ng = false;
            do b = Read();
            while (b != '-' && (b < '0' || '9' < b));
            if (b == '-') { ng = true; b = Read(); }
            for (; true; b = Read())
            {
                if (b < '0' || '9' < b)
                    return ng ? -ret : ret;
                else ret = ret * 10 + b - '0';
            }
        }
        
        public int Integer() { return (int)Long(); }
        public double Double() { return double.Parse(Scan(), CultureInfo.InvariantCulture); }
    }
}