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.

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

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.

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

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