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: Wrong Answer)

#![allow(unused_imports)]
#![allow(dead_code)]
#![allow(unused_must_use)]
use std::io::{stdin, stdout, stderr, Write, BufWriter, BufReader, BufRead};
use std::collections::BinaryHeap;

use util::IterExt;
macro_rules! read_from_line {
    ($inbuf:ident => $($name:ident : $ty:ty),* ) => {
        let mut buf = String::new();
        $inbuf.read_line(&mut buf).unwrap();
        buf.pop();
        let mut words = buf.split_whitespace();
        $(
            let $name:$ty = words.next().unwrap().parse().unwrap();
        )*
    };
}

macro_rules! read_many {
    ($inbuf:ident => $name:ident : $ty:ty) => {
        let $name: Vec<$ty> = strio::read_many_from_line(&mut $inbuf);
    };
}

fn gcd(a: i64, b:i64) -> i64 {
    let mut a = a;
    let mut b = b;
    if a > b {
        std::mem::swap(&mut a, &mut b);
    }
    while a != 0 {
        b %= a;
        std::mem::swap(&mut a, &mut b);
    }

    b
}

fn check(a: i64, b:i64, c:i64, d:i64) -> bool {
    //println!("in {} {} {} {}", a, b, c, d);
    if a < b || b > d{ return false; }
    if b <= c {
        return true;
    }
    let mut a = a;
    if a <= c {
        a = a - b + d;
    }
    a = a - b * ((a - c) / b);
    while a > c {
        a -= b;
    }
    //println!("newa {}", a);
    let x = gcd(b, d);
    //println!("gcd {}", x);
    if x == 0 {
        return true;
    }
    let n = a + d % b;
    //println!("n {}", n);
    let s = n + (c - n) / x * x;
    //println!("s {}", s);
    if s + x < b {
        return false;
    } else {
        return true;
    }


}

fn solve() {
    let cout = stdout();
    let mut cout = BufWriter::new(cout.lock());
    let cin = stdin();
    let mut cin = BufReader::new(cin.lock());
    read_from_line!(cin => t: i64);
    for _i in 0..t {
        read_from_line!(cin => a: i64, b:i64, c:i64, d:i64);
        if check(a, b, c, d) {
            writeln!(cout, "YES");
        } else {
            writeln!(cout, "NO");
        }

    }
}

fn main() {
    let stack_size = 100 * 1024 * 1024;
    let thread = std::thread::Builder::new().stack_size(stack_size);
    thread.spawn(|| solve()).unwrap().join().unwrap();
}

mod util {
    use std;
    use std::ops::{Deref, AddAssign};
    use std::iter::{Once, Chain, Scan};
    use std::borrow::Borrow;

    pub trait IterExt where
        Self: Iterator
    {
        fn scan_init<'a, St : 'a, F : 'a> (self, initial_state: St, f: F) -> Box<Iterator<Item=St> + 'a> /*Chain<Once<St>, Scan<Self, St, F>>*/  where
            Self: Sized + 'a,
            F: FnMut(&mut St, Self::Item) -> Option<St>,
            St: Clone
        {
            Box::new(std::iter::once(initial_state.clone()).chain(self.scan(initial_state, f)))
        }

        fn accum<'a, T> (self, init: T) -> Box<Iterator<Item=T> + 'a> where
            Self: Sized + 'a,
            Self::Item: Borrow<T>,
            T: Clone + AddAssign + 'a,
        {
            Box::new(self.scan_init(init, |sum, x| { *sum += x.borrow().clone(); Some(sum.clone()) }))
        }
    }

    impl<T> IterExt for T where
        T: Iterator
    { }

    pub fn test()
    {
        let v:Vec<i32> = vec![1, 4 ,2];
        for x in v.iter().accum(0) {
            println!("{}", x);
        }
        for x in v.iter().accum(0).accum(0) {
            println!("{}", x);
        }

    }

}

mod strio {
    use std::str::FromStr;
    use std;

    pub fn read_from_line<T, R> (r: &mut R) -> T where
        T: FromStr,
        <T as std::str::FromStr>::Err : std::fmt::Debug,
        R: std::io::BufRead,
    {
        let mut buf = String::new();
        r.read_line(&mut buf).unwrap();
        buf.pop();
        buf.parse().unwrap()
    }

    pub fn read_many_from_line<T, R> (r: &mut R) -> Vec<T> where
        T: FromStr,
        <T as std::str::FromStr>::Err : std::fmt::Debug,
        R: std::io::BufRead,
    {
        let mut buf = String::new();
        r.read_line(&mut buf).unwrap();
        buf.pop();
        buf.split_whitespace().map(|x| x.parse().unwrap()).collect()
    }
}