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"
)

////////////////////////////////////////
///        templates                 ///
////////////////////////////////////////

var sc = bufio.NewScanner(os.Stdin)

func nextLine() string {
        sc.Scan()
        return sc.Text()
}

var rdr = bufio.NewReaderSize(os.Stdin, 1000000)

func readBigLine() string {
        buf := make([]byte, 0, 1000000)
        for {
                l, p, e := rdr.ReadLine()
                if e != nil {
                        panic(e)
                }
                buf = append(buf, l...)
                if !p {
                        break
                }
        }
        return string(buf)
}

func strSprit(str string) []string {
        cols := strings.Split(str, " ")
        return cols
}

func parseInt(str string) int {
        n, _ := strconv.Atoi(str)
        return n
}

func intSprit(str string) []int {
        strs := strSprit(str)
        cols := make([]int, len(strs))
        for i, v := range strs {
                cols[i] = parseInt(v)
        }
        return cols
}

type SortSlice []int

func (s SortSlice) Len() int {
        return len(s)
}

func (s SortSlice) Swap(i, j int) {
        s[i], s[j] = s[j], s[i]
}

func (s SortSlice) Less(i, j int) bool {
        return s[i] < s[j]
}

func reverseString(str string) string {
        buf := []rune(str)
        for i, j := 0, len(buf)-1; i < j; i, j = i+1, j-1 {
                buf[i], buf[j] = buf[j], buf[i]
        }
        return string(buf)
}

////////////////////////////////////////
///        end templates             ///
////////////////////////////////////////

func parseInt64(str string) int64 {
        n, _ := strconv.ParseInt(str, 10, 64)
        return n
}

func main() {
        line := nextLine()
        T := parseInt(line)

        for i := 0; i < T; i++ {
                m := map[int64]bool{}
                l := nextLine()
                spl := strSprit(l)
                A := parseInt64(spl[0])
                B := parseInt64(spl[1])
                C := parseInt64(spl[2])
                D := parseInt64(spl[3])

                a := A % B
                ans := false

                if A < B {
                        fmt.Println("No")
                        continue
                }
                cnt := 0

                for cnt < 100000 {
                        cnt++
                        r := a % B
                        if r > C {
                                break
                        }
                        if B > D && a <= 0 {
                                break
                        }
                        a += D - B
                        a %= B

                        if m[r] {
                                ans = true
                                break
                        }
                        m[r] = true

                }

                if ans {
                        fmt.Println("Yes")
                } else {
                        fmt.Println("No")
                }
        }
}