Problem: 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.

Examples

Input

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


Output

No
Yes
No
Yes
Yes
No
No
Yes
No
Yes
Yes
No
No
Yes


Input

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


Output

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 JAVA):

Solution:
import java.util.*;

public class Main{

	public static void main(String[] args){
	
		Scanner scan = new Scanner(System.in);
		
		int allNum = scan.nextInt();
		
		long fStock = 0;
		long buy = 0;
		long aCheck = 0;
		long pStock = 0;
		
		for(int i=0; i < allNum; i++){
			
			fStock = scan.nextLong();
			buy = scan.nextLong();
			aCheck = scan.nextLong();
			pStock = scan.nextLong();
			
			if(check(fStock,buy,aCheck,pStock)) System.out.println("Yes");
			else System.out.println("No");
			
		}
		scan.close();
	
	}	
	
	private static boolean check(long fStock,long buy,long aCheck,long pStock){
		
		if(fStock < buy) return false;
		if(buy > pStock) return false;
		if(aCheck >= buy) return true;
		
		long ba = baCheck(buy,pStock);
		
		if(buy - ba + (fStock % ba) > aCheck) return false;
		else return true;
	}
	
	private static long baCheck(long buy,long pStock){
		long c = buy % pStock;
		if(c==0) return pStock;
		return baCheck(pStock,c);
	}

}