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 static System.Console;
using static System.Math;
using System.Collections.Generic;
using System.Linq;

class Program
{
    public static void Main()
    {
        int T = int.Parse(ReadLine());
        ulong[] a = new ulong[T];
        ulong[] b = new ulong[T];
        ulong[] c = new ulong[T];
        ulong[] d = new ulong[T];
        foreach (int i in EnumerableCommon.Range(T))
        {
            var input = ReadLine().Split();
            a[i] = ulong.Parse(input[0]);
            b[i] = ulong.Parse(input[1]);
            c[i] = ulong.Parse(input[2]);
            d[i] = ulong.Parse(input[3]);
        }
        ulong stock = 0;
        foreach (int i in EnumerableCommon.Range(T))
        {
            bool ok = true;
            if (b[i] <= a[i] && b[i] <= d[i] && (a[i] % b[i] <= c[i]))
            {
                stock = a[i] % b[i];
                int sameCount = 0;
                while (true)
                {
                    if (sameCount == 3)
                    {
                        ok = true;
                        break;
                    }
                    ulong temp = stock;

                    //昼
                    if (stock > c[i])
                    {
                        ok = false;
                        break;
                    }
                    else if (stock == 0)
                    {
                        ok = true;
                        break;
                    }
                    //夜
                    if (stock <= c[i]) { stock = (stock + d[i]) % b[i]; }
                    if (stock == temp) sameCount++;
                    else sameCount = 0;
                }
            }
            else ok = false;
            if (ok) WriteLine("Yes");
            else WriteLine("No");
        }
    }

    public static partial class EnumerableCommon
    {
        public static IEnumerable<int> Range(int count)
        {
            return Enumerable.Range(0, count);
        }
    }
}