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.Linq;
//using System.Text;
class P
{
    static List<long> Checked = new List<long>();
    static void Main()
    {
        int t = int.Parse(Console.ReadLine());
        for (int i = 0; i < t; i++)
        {
            long a, b, c, d;
            string[] s = Console.ReadLine().Split();
            a = long.Parse(s[0]);
            b = long.Parse(s[1]);
            c = long.Parse(s[2]);
            d = long.Parse(s[3]);
            //Console.WriteLine(String.Format("{0} {1} {2} {3}", a, b, c, d));
            Solv(a, b, c, d);
            Checked = new List<long>();
        }
    }
    static void Solv(long a, long b, long c, long d)
    {
        if (a < b)
        {
            Console.WriteLine("No");
            return;
        }
        if (c >= b && d >= b)
        {
            Console.WriteLine("Yes");
            return;
        }
        long apn = a - b;
        if ((c < apn && apn < b) || (apn < b - d))
        {
            Console.WriteLine("No");
            return;
        }
        if (Checked.Contains(a))
        {
            Console.WriteLine("Yes");
            return;
        }
        Checked.Add(a);
        //Console.WriteLine(a);
        if (a > c)
        {
            a %= b;
            long n = c / b;
            a += n * b;
        }
        if (a <= c)
            a += d;
        //Console.WriteLine(a);
        Solv(a, b, c, d);
    }
}