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.Linq;
using System.Text;
using System.IO;
using System.Runtime.Remoting.Contexts;

namespace Contest
{
    class Scanner
    {
        private string[] line = new string[0];
        private int index = 0;

        public string Next()
        {
            if (line.Length <= index)
            {
                line = Console.ReadLine().Split(' ');
                index = 0;
            }

            var res = line[index];
            index++;
            return res;
        }

        public int NextInt()
        {
            return int.Parse(Next());
        }

        public long NextLong()
        {
            return long.Parse(Next());
        }

        public string[] Array()
        {
            line = Console.ReadLine().Split(' ');
            index = line.Length;
            return line;
        }

        public int[] IntArray(int n)
        {
            var array = Array();
            var result = new int[n];
            for (int i = 0; i < n; i++)
            {
                result[i] = int.Parse(array[i]);
            }

            return result;
        }

        public int[] IntArray()
        {
            var array = Array();
            var result = new int[array.Length];
            for (int i = 0; i < array.Length; i++)
            {
                result[i] = int.Parse(array[i]);
            }

            return result;
        }


        public long[] LongArray()
        {
            var array = Array();
            var result = new long[array.Length];
            for (int i = 0; i < array.Length; i++)
            {
                result[i] = long.Parse(array[i]);
            }

            return result;
        }

        public uint NextUint()
        {
            return uint.Parse(Next());
        }
    }

    class Program
    {
        private Scanner Sc;
        private int N;
        public void Solve()
        {
            Sc = new Scanner();
            N = Sc.NextInt();
            var sb = new StringBuilder();
            for (int i = 0; i < N; i++)
            {
                long a = Sc.NextLong();
                long b = Sc.NextLong();
                long c = Sc.NextLong();
                long d = Sc.NextLong();
                if (Q(a, b, c, d))
                {
                    sb.AppendLine("Yes");
                }
                else
                {
                    sb.AppendLine("No");
                }
            }
            Console.Write(sb.ToString());
        }

        public long GCD(long a, long b)
        {
            while (b > 0)
            {
                var r = b;
                b = a % b;
                a = r;
            }
            return a;
        }

        private bool Q(long a, long b, long c, long d)
        {
            if (a < b) return false;
            if (d < b) return false;
            if (c < b)
            {
                //C<(A+ND)%Bならfalse
                //  Console.WriteLine($"{a} {b} {c} {d}");
                long gcd = GCD(b, d);
                long m = a % b;
               // Console.WriteLine(gcd);
                if (c < m) return false;
                //plus
                {

                    long def = b - m;
                    long dev;
                    if (def % gcd == 0)
                    {
                        dev = (def - gcd) / gcd;
                    }
                    else
                    {
                        dev = (def) / gcd;
                    }
                    if (c < m + dev * gcd) return false;
                }

                //minus;
                {
                    long dev;

                    dev = (m + gcd) / gcd;

                    long res = m - dev * gcd + b;
                    if (c < res) return false;
                }
            }

            return true;
        }

        static void Main() => new Program().Solve();
    }
}