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: Time Limit Exceeded)

using System;
using System.Linq;

namespace AGC026_B
{
    class Program
    {
        static void Main(string[] args)
        {
            var T = int.Parse(Console.ReadLine());
            for (int i = 0; i < T; i++)
            {
                var input = Console.ReadLine().Split().Select(long.Parse).ToArray();
                long A = input[0];
                long B = input[1];
                long C = input[2];
                long D = input[3];
                bool p = true;

                if (A < B || B > D)
                {
                    Console.WriteLine("No");
                    continue;
                }

                A = A % B + B;
                D = D % B + B;

                if (B == D)
                {
                    if (A - B > C)
                    {
                        p = false;
                    }
                }
                else if (B - C == 1)
                {
                }
                else if (B - C == 2 && B % 2 == 0 && D % 2 == 0)
                {
                }
                else if (B - C >= SamePrime(B, D) + 1)
                {
                    p = false;
                }

                Console.WriteLine(p ? "Yes" : "No");
            }
        }

        private static int SamePrime(long n1, long n2)
        {
            if (n1 % 2 == 0 && n2 % 2 == 0)
            {
                return 2;
            }
            for (int i = 3; i <= Math.Min(Math.Sqrt(n1), Math.Sqrt(n2)); i+=2)
                if (n1 % i == 0 && n2 % i == 0)
                {
                    return i;
                }
            return 1;
        }
    }
}