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 Rust (1.15.1) (judge verdict: Time Limit Exceeded)

use std::cmp::*;
use std::io::*;
use std::str::FromStr;
use utils::*;

pub fn main() {
    let i = stdin();
    let mut o = Vec::new();
    run(i.lock(), &mut o);
    stdout().write_all(&o).unwrap();
}

fn run<R: BufRead, W: Write>(i: R, o: &mut W) {
    let mut i = CpReader::new(i);
    let t = i.read::<usize>();
    let mut primes = Primes::new();
    for _ in 0..t {
        let (a, b, c, d) = i.read4::<usize, usize, usize, usize>();
        let result = if solve(a, b, c, d, &mut primes) {
            "Yes"
        } else {
            "No"
        };
        writeln!(o, "{}", result).unwrap();
    }
}
fn solve(mut a: usize, b: usize, c: usize, d: usize, primes: &mut Primes) -> bool {
    if a < b || d < b {
        return false;
    }
    if c >= b {
        return true;
    }
    a -= b;
    if a <= c {
        a += d;
    }
    let mut x = a - c - 1;
    let xt = b - c - 1;
    if xt == 0 {
        return true;
    }

    x -= x / b * b;
    if x < xt {
        return false;
    }

    let x0 = x;

    x += d - b;
    x -= x / b * b;
    if x < xt {
        return false;
    }
    let x1 = x;

    let xd = if x1 >= x0 { x1 - x0 } else { b + x0 - x1 };
    if xd == 0 {
        return true;
    }
    if primes.is_co_prime(b, xd) {
        return false;
    }

    if xd < b / 2 {
        x += ((b - x - 1) / xd + 1) * xd;
        x %= b;
        let x0 = x;
        if x < xt {
            return false;
        }

        loop {
            x += ((b - x - 1) / xd + 1) * xd;
            x %= b;
            if x < xt {
                return false;
            }
            if x == x0 {
                return true;
            }
        }
    } else {
        x -= x / xd * xd;
        if x < xt {
            return false;
        }
        let x0 = x;
        loop {
            x += b;
            x -= x / xd * xd;
            if x < xt {
                return false;
            }
            if x == x0 {
                return true;
            }
        }
    }
}

struct Primes {
    is_prime: Vec<bool>,
    primes: Vec<usize>,
}

impl Primes {
    fn new() -> Self {
        Primes {
            is_prime: vec![false, true],
            primes: Vec::new(),
        }
    }
    fn ready(&mut self, n: usize) {
        loop {
            let len = self.is_prime.len();
            if len > n {
                return;
            }
            let mut is_prime = true;
            for &p in &self.primes {
                if len % p == 0 {
                    is_prime = false;
                    break;
                }
            }
            if is_prime {
                self.primes.push(len);
            }
            self.is_prime.push(is_prime);
        }
    }
    fn is_co_prime(&mut self, n0: usize, n1: usize) -> bool {
        self.ready(max(n0, n1));
        for &p in &self.primes {
            if n0 % p != 0 && n1 % p != 0 {
                return false;
            }
        }
        true
    }
}

mod utils {
    use super::*;

    pub struct CpReader<R: BufRead> {
        r: R,
        s: String,
    }

    macro_rules! fn_read {
        {$f:ident($($v:ident: $t:ident),*)} => {
            pub fn $f<$($t: FromStr),*>(&mut self) -> ($($t),*) {
                let i = &mut self.read_line().split(' ');
                $(
                    let $v = i.next().unwrap().parse().ok().unwrap();
                )*
                ($($v),*)
            }
        };
    }

    impl<R: BufRead> CpReader<R> {
        pub fn new(r: R) -> Self {
            CpReader {
                r: r,
                s: String::new(),
            }
        }
        pub fn read_line(&mut self) -> &str {
            self.s.clear();
            self.r.read_line(&mut self.s).unwrap();
            self.s.trim()
        }

        pub fn read<T: FromStr>(&mut self) -> T {
            self.read_line().parse().ok().unwrap()
        }
        fn_read! { read4(v1: T1, v2: T2, v3: T3, v4: T4) }
    }
}