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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
	"strings"
)

var sc = bufio.NewScanner(os.Stdin)
var input = make([]string, 0)
var initA = 0
var inputLimit = 1

func main() {
	i := 0
	for sc.Scan() {
		i++
		input = append(input, sc.Text())

		l, _ := strconv.Atoi(input[0])
		inputLimit = l + 1
		if i == inputLimit {
			break
		}
	}

	in := input[1:]
	for i := range in {
		a, b, c, d := splitSpace(in[i])
		initA = a
		days(a, b, c, d)
	}
}

// func oneDay(a, b, c, d int) {
// 	var nextA int
// 	if a-b <= c {
// 		nextA = a - b + d
// 	} else {
// 		nextA = a - b
// 	}

// 	if nextA < b {
// 		fmt.Println("No")
// 	} else if nextA == initA {
// 		fmt.Println("Yes")
// 	} else {
// 		oneDay(nextA, b, c, d)
// 	}
// }

func days(a, b, c, d int) {
	var nextA int
	for {

		if c+d == a {
			fmt.Println("Yes")
			return
		} else if c+d == a-1 {
			fmt.Println("No")
			return
		}

		if (a - b) < 0 {
			fmt.Println("No")
			return
		}

		if a-b <= c {
			nextA = a - b + d
		} else {
			if a-b == c {
				fmt.Println("Yes")
				return
			}
			nextA = a - b
		}

		if nextA < b {
			fmt.Println("No")
			break
		} else if nextA == initA {
			fmt.Println("Yes")
			break
		} else {
			a = nextA
		}
	}
}

func splitSpace(input string) (a, b, c, d int) {
	s := strings.Split(input, " ")
	a, _ = strconv.Atoi(s[0])
	b, _ = strconv.Atoi(s[1])
	c, _ = strconv.Atoi(s[2])
	d, _ = strconv.Atoi(s[3])
	return a, b, c, d
}