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.*;
import java.io.*;

public class Main {
    public static long gcd(long x, long y){
        if(x<y) return gcd(y,x);
        if(y==0)return x;
        return gcd(y,x%y);
    }
    public static long buy(long current, long pace, long limit){
        long day = (current-limit)/pace;
        long ans = current-pace*day;
        if(ans>limit)ans-=pace;
        return ans;
    }
    public static long store(long current, long pace, long limit){
        long day = (limit-current)/pace;
        long ans = current+pace*day;
        if(ans<limit) ans+=pace;
        return ans;
    }
    public static boolean solve(long A, long B, long C, long D){
        long g = gcd(B,D);
        return solve_dis(A/g, B/g, C/g - (A%B>C ? 1 : 0), D/g);
    }
    public static boolean solve_dis(long A, long B, long C, long D){
        if(A<B) {
        	//System.out.println("sold out on first day.");
        	return false;
        }
        if(B>D) {
        	//System.out.println("snuke drink too much.");
        	return false;
        }
        
        
        if(B>C+1){
        	//System.out.println("unfortunately sold out.");
        	return false;
        }
        //System.out.println("snuke will buy apple juice forever.");
        return true;
    }
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int T = sc.nextInt();
        for(int t=0;t<T;t++) 
            System.out.println(solve(sc.nextLong(),sc.nextLong(),sc.nextLong(),sc.nextLong()) ? "Yes" : "No");
    }
}