Problem:
Score : 100 points

Problem Statement

In this problem, you should process T testcases.

For each testcase, you are given four integers N, M, A, B.

Calculate \sum_{i = 0}^{N - 1} floor((A \times i + B) / M).

Constraints

1 \leq T \leq 100,000

1 \leq N, M \leq 10^9

0 \leq A, B < M

Input

Input is given from Standard Input in the following format:

T
N_0 M_0 A_0 B_0
N_1 M_1 A_1 B_1
:
N_{T - 1} M_{T - 1} A_{T - 1} B_{T - 1}

Output

Print the answer for each testcase.

Sample Input 1

5
4 10 6 3
6 5 4 3
1 1 0 0
31415 92653 58979 32384
1000000000 1000000000 999999999 999999999

Sample Output 1

3
13
0
314095480
499999999500000000

Solution in Rust (1.42.0) (judge verdict: Accepted)

#![allow(unused_imports)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;
use std::ops::Bound::*;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn main() {
    let t = read::<usize>();
    for i in 0..t {
        let v = read_vec::<i64>();
        let (n, m, a, b) = (v[0], v[1], v[2], v[3]);
        let ans = floor_sum(n, m, a, b);
        println!("{}", ans);
    }
}

fn floor_sum(n: i64, m: i64, a: i64, b: i64) -> i64 {
    fn internal(n: i64, m: i64, mut a: i64, mut b: i64, mut acc: i64) -> i64 {
        if a >= m {
            let q = a / m;
            acc += (n - 1) * n / 2 * q;
            a -= q * m;
        }
        if b >= m {
            let q = b / m;
            acc += n * q;
            b -= q * m;
        }
        let y_max = (a * n + b) / m;
        let x_max = y_max * m - b;
        if y_max == 0 {
            return acc;
        }
        acc += (n - (x_max + a - 1) / a) * y_max;
        let mut sub_b = a - x_max % a;
        if sub_b >= a {
            sub_b -= a;
        }
        internal(y_max, a, m, sub_b, acc)
    }
    internal(n, m, a, b, 0)
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}