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

namespace Practice
{
    class Program
    {
        static void Main(string[] args)
        {
            //SolveA(args);
            SolveB(args);
            //SolveC(args);
            //SolveD(args);


        }
        public struct Query
        {
            public long a;
            public long b;
            public long c;
            public long d;
        }
        static void SolveB(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            long[][] q = new long[n][];
            for (int i = 0; i < n; ++i)
            {
                q[i] = Array.ConvertAll(Console.ReadLine().Split(' '), long.Parse);
            }

            
            for(int i=0;i<n;++i)
            {
                if( Check(q[i]))
                {
                    Console.WriteLine("Yes");
                }
                else
                {
                    Console.WriteLine("No");
                }
            }
        }

        static bool Check(long[] q )
        {
            long errorCnt = 0;
            long a = q[0];
            long b = q[1];
            long c = q[2];
            long d = q[3];
            long start = a;
            while(true)
            {
                long n = (long)Math.Ceiling((decimal)(a - c) / b);
                if (n <= 0) { n = 1; }
                a = a - b * n;
                if( a < 0) { return false; }
                if( a > c)
                {
                    Console.WriteLine("Error2");
                    return false;
                }
                a += d;
                if( a == start) { return true; }
                errorCnt++;
                if( errorCnt >= int.MaxValue)
                {
                    //Console.WriteLine("Error");
                    return true;

                }
            }
        }
    }
}