// ax - by = k
// by - ax = k

use std::io::Write;

fn run() {
    input! {
        t: usize,
        ask: [(u64, u64, u64, u64); t],
    }
    let calc = |m: u64, a: u64, b: u64, k: u64| -> u64 {
        let g = binary_gcd(a, b);
        let m = m / g;
        let a = a / g;
        let b = b / g;
        if k % g != 0 {
            return 0;
        }
        let k = k / g;
        let lcm = a * b;
        let mut ans = 0;
        if k == a {
            ans += m / lcm * (b - a + 1) - 1;
            let m = m % lcm;
            let x = m / a;
            let y = m / b;
            ans += x - y;
        } else if k < a {
            ans += m / lcm * 2;
            let p = inv(((a * b - b) % a) as i64, a as i64) as u64;
            let y = k * p % a;
            let x = (k + b * y) / a;
            if a * x <= m % lcm {
                ans += 1;
            }
            let p = inv((b % a) as i64, a as i64) as u64;
            let y = k * p % a;
            if b * y <= m % lcm {
                ans += 1;
            }
        }
        ans
    };
    let out = std::io::stdout();
    let mut out = std::io::BufWriter::new(out.lock());
    for (m, a, b, k) in ask {
        writeln!(out, "{}", calc(m, a, b, k)).ok();
    }
}

fn main() {
    run();
}

// a * x = 1 (mod m)
pub fn inv(a: i64, m: i64) -> i64 {
    if a == 1 {
        1
    } else {
        m + (-m * inv(m % a, a) + 1) / a
    }
}

// ---------- begin binary_gcd ----------
pub fn binary_gcd(a: u64, b: u64) -> u64 {
    if a == 0 || b == 0 {
        return a + b;
    }
    let x = a.trailing_zeros();
    let y = b.trailing_zeros();
    let mut a = a >> x;
    let mut b = b >> y;
    while a != b {
        let x = (a ^ b).trailing_zeros();
        if a < b {
            std::mem::swap(&mut a, &mut b);
        }
        a = (a - b) >> x;
    }
    a << x.min(y)
}
// ---------- end binary_gcd ----------
// ---------- begin input macro ----------
// reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
#[macro_export]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

#[macro_export]
macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};
    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

#[macro_export]
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };
    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };
    ($iter:expr, bytes) => {
        read_value!($iter, String).bytes().collect::<Vec<u8>>()
    };
    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };
    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}
// ---------- end input macro ----------