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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.HashSet;
import java.util.Set;
import java.io.IOException;
import java.util.NoSuchElementException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		Scanner in = new Scanner(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskB solver = new TaskB();
		solver.solve(1, in, out);
		out.close();
	}

	static class TaskB {
		public void solve(int testNumber, Scanner sc, PrintWriter out) {

			int t = sc.nextInt();

			for (int i = 0; i < t; i++) {
				long a = sc.nextLong();
				long b = sc.nextLong();
				long c = sc.nextLong();
				long d = sc.nextLong();

				Set<Long> set = new HashSet<>();
				long prev = -1145141919810364364l, diff = -1145141919810364364l;

				long stock = a;

				while (true) {
					if (stock < b) {
						out.println("No");
						break;
					}
					long tmp = stock % b;
					if (tmp <= c) {
						stock = Math.min(stock - b, tmp + (c - tmp) / b * b);
						stock += d;
						if (stock > prev && diff == stock - prev) {
							stock = c + d;
						}
					} else {
						stock = tmp;
					}
					diff = stock - prev;
					prev = stock;

					if (set.contains(stock)) {
						out.println("Yes");
						break;
					} else {
						set.add(stock);
					}
				}
			}

		}

	}

	static class Scanner {
		private final InputStream in;
		private final byte[] buffer;
		private int ptr;
		private int buflen;

		public Scanner(InputStream in) {
			this.in = in;
			this.buffer = new byte[1024];
			this.ptr = 0;
			this.buflen = 0;
		}

		private boolean hasNextByte() {
			if (ptr < buflen) return true;
			else {
				ptr = 0;
				try {
					buflen = in.read(buffer);
				} catch (IOException e) {
					e.printStackTrace();
				}
				if (buflen <= 0) return false;
			}
			return true;
		}

		private byte readByte() {
			if (hasNextByte()) return buffer[ptr++];
			return -1;
		}

		private boolean isPrintableChar(byte c) {
			return '!' <= c && c <= '~';
		}

		private void skipUnprintable() {
			while (hasNextByte() && !isPrintableChar(buffer[ptr])) {
				ptr++;
			}
		}

		public boolean hasNext() {
			skipUnprintable();
			return hasNextByte();
		}

		public int nextInt() {
			if (!hasNext()) throw new NoSuchElementException();
			int n = 0;
			boolean minus = false;
			byte b = readByte();
			if (b == '-') {
				minus = true;
				b = readByte();
			}
			if (b < '0' || '9' < b) throw new NumberFormatException();
			while (true) {
				if ('0' <= b && b <= '9') {
					n *= 10;
					n += b - '0';
				} else if (b == -1 || !isPrintableChar(b)) {
					return minus ? -n : n;
				} else {
					throw new NumberFormatException();
				}
				b = readByte();
			}
		}

		public long nextLong() {
			if (!hasNext()) throw new NoSuchElementException();
			long n = 0;
			boolean minus = false;
			byte b = readByte();
			if (b == '-') {
				minus = true;
				b = readByte();
			}
			if (b < '0' || '9' < b) throw new NumberFormatException();
			while (true) {
				if ('0' <= b && b <= '9') {
					n *= 10;
					n += b - '0';
				} else if (b == -1 || !isPrintableChar(b)) {
					return minus ? -n : n;
				} else {
					throw new NumberFormatException();
				}
				b = readByte();
			}
		}

	}
}