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: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;

public class Main {

	public static void main(String[] args) {
		IO io = new IO();
		int t = io.nextInt();
		for(int tt=0;tt<t;tt++) {
			long a = io.nextLong();
			long b = io.nextLong();
			long c = io.nextLong();
			long d = io.nextLong();
			io.println(check(a,b,c,d) ? "Yes" : "No");
		}
		io.flush();
	}
	public static boolean check(long a, long b, long c, long d) {
		if (d < b) return false;
		if (d == b) {
			if (a <= c) {
				return a - b >= 0;
			}else {
				return a % b <= c;
			}
		}
		if (a < c && a - b < 0) {
			return false;
		}
		long g = Gcd.gcd(b, d);
		long x = higherMultiple(c-a-b, g) + a;
		return x >= 0;
	}
	public static long higherMultiple(long a, long m) {
		long x = a / m * m;
		if (a >= 0 || a % m == 0) {
			x += m;
		}
		return x;
	}
}
class Gcd {
	public static long gcd(long a,long b) {
		while(b!=0) {
			long r = a%b;
			a = b;
			b = r;
		}
		return a;
	}
	public static long lcm(long a,long b) {
		return a / gcd(a,b) * b;
	}

	/**
	 *  @return [x,y,gcd(a,b)]
	 *  where ax + by = gcd(a,b), |x| <= b, |y| <= a
	 */
	public static long[] extgcd(long a,long b) {
		long[] u = {1,0,a}, v = {0,1,b};
		while(v[2] > 0) {
			long t = u[2] / v[2];
			u[0] -= t * v[0];
			u[1] -= t * v[1];
			u[2] -= t * v[2];
			long[] temp = u;
			u = v;
			v = temp;
		}
		return u;
	}
}
class IO extends PrintWriter {
	private final InputStream in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;

	public IO() {
		this(System.in);
	}

	public IO(InputStream source) {
		super(System.out);
		this.in = source;
	}

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

	private static boolean isPrintableChar(int c) {
		return 33 <= c && c <= 126;
	}

	private static boolean isNewLine(int c) {
		return c == '\n' || c == '\r';
	}

	public boolean hasNext() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr]))
			ptr++;
		return hasNextByte();
	}

	public boolean hasNextLine() {
		while (hasNextByte() && isNewLine(buffer[ptr]))
			ptr++;
		return hasNextByte();
	}

	public String next() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	public char[] nextCharArray(int len) {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		char[] s = new char[len];
		int i = 0;
		int b = readByte();
		while (isPrintableChar(b)) {
			if (i == len) {
				throw new InputMismatchException();
			}
			s[i++] = (char) b;
			b = readByte();
		}
		return s;
	}

	public String nextLine() {
		if (!hasNextLine()) {
			throw new NoSuchElementException();
		}
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (!isNewLine(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	public long nextLong() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		long n = 0;
		boolean minus = false;
		int 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 int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) {
			throw new NumberFormatException();
		}
		return (int) nl;
	}

	public char nextChar() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		return (char) readByte();
	}

	public double nextDouble() {
		return Double.parseDouble(next());
	}

	public int[] nextIntArray(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = nextInt();
		return a;
	}

	public long[] nextLongArray(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = nextLong();
		return a;
	}

	public double[] nextDoubleArray(int n) {
		double[] a = new double[n];
		for (int i = 0; i < n; i++)
			a[i] = nextDouble();
		return a;
	}

	public void nextIntArrays(int[]... a) {
		for (int i = 0; i < a[0].length; i++)
			for (int j = 0; j < a.length; j++)
				a[j][i] = nextInt();
	}

	public int[][] nextIntMatrix(int n, int m) {
		int[][] a = new int[n][];
		for (int i = 0; i < n; i++)
			a[i] = nextIntArray(m);
		return a;
	}

	public char[][] nextCharMap(int n, int m) {
		char[][] a = new char[n][];
		for (int i = 0; i < n; i++)
			a[i] = nextCharArray(m);
		return a;
	}

	public void close() {
		super.close();
		try {
			in.close();
		} catch (IOException e) {
		}
	}
}