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 Java7 (OpenJDK 1.7.0) (judge verdict: Accepted)


import java.util.HashSet;
import java.util.Scanner;
import java.util.Set;

public class Main {

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);
		int T = sc.nextInt();
		long A[] = new long[T];
		long B[] = new long[T];
		long C[] = new long[T];
		long D[] = new long[T];
		for (int i = 0; i < T; i++) {
			A[i] = sc.nextLong();
			B[i] = sc.nextLong();
			C[i] = sc.nextLong();
			D[i] = sc.nextLong();
		}
		for (int i = 0; i < T; i++) {
			Long AA = A[i];
			Long BB = B[i];
			Long CC = C[i];
			Long DD = D[i];
			boolean JG = true;
			if (AA < BB || DD < BB) {
				JG = false;
			} else if (CC >= BB) {
				JG = true;
			} else {
				Set<Long> set = new HashSet<>();
				Long A1 = AA % BB;
				set.add(A1);
				if (A1 > CC) {
					JG = false;
				} else {
					Long D2 = DD % BB;
					A1 += D2;
					while (true) {
						//System.out.println(A1);
						if (A1 >= BB) {
							A1 -= BB;
						}
						if (A1 > CC) {
							JG = false;
							break;
						} else {
							if (D2 == 0) {
								JG = true;
								break;
							}
							long k = (BB - A1) / D2;
							if(A1 + (D2 * k) == BB){
								k--;
							}
							if (A1 + (D2 * k) > CC && A1 + (D2 * k) != BB) {
								JG = false;
								break;
							} else {
								A1 = A1 + (D2 * (k + 1)) - BB;
								if (set.contains(A1)) {
									JG = true;
									break;
								} else {
									set.add(A1);
								}
							}
						}
					}
				}
			}
			if (JG) {
				System.out.println("Yes");

			} else {
				System.out.println("No");

			}
		}

	}
}