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Contest: Task: Related: TaskA TaskC

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