Problem:
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

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

module Main where

import Control.Applicative
import Control.Exception (assert)
import Control.Monad

data Test = Test Integer Integer Integer Integer
          deriving (Show, Eq)
data Result = Yes | No
            deriving (Show, Eq)

solve :: Test -> Result
solve (Test a b c d) | d < b = No
                     | a < b = No
                     | c >= b = Yes
                     | k1 < n && a1 > c = No
                     | k2 < n && a2 > c = No
                     | otherwise = Yes
    where a' = a `mod` b
          g = b `gcd` d
          n = b `div` g

          k1 = (b - 1 - a') `div` g
          k2 = n - 1

          a1 = (a + k1 * g) `mod` b
          a2 = (a + k2 * g) `mod` b
          -- (a' + k * g) mod b <= c, where k in [0, n).
          -- For all k: k * g < b, a' < b. Therefore, a' + k * g < 2 * b
          -- a' + k * g < b => a' + k * g + 1 <= b => k <= (b - 1 - a') `div` g

tests = [Test 9 7 5 9,
         Test 9 7 6 9,
         Test 14 10 7 12,
         Test 14 10 8 12,
         Test 14 10 9 12,
         Test 14 10 7 11,
         Test 14 10 8 11,
         Test 14 10 9 11,
         Test 9 10 5 10,
         Test 10 10 5 10,
         Test 11 10 5 10,
         Test 16 10 5 10,
         Test 1000000000000000000 17 14 999999999999999985,
         Test 1000000000000000000 17 15 999999999999999985] :: [Test]

main :: IO ()
main = do
  numTests <- read <$> getLine
  replicateM_ numTests $ do
         [a, b, c, d] <- map read . words <$> getLine
         print $ solve (Test a b c d)