rng_10s

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

inputFormat

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.

outputFormat

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

样例

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

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