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 Ruby (2.7.1) (judge verdict: Accepted)

def floor_sum(n, m, a, b)
  ans = 0

  if a >= m
    ans += (n - 1) * n * (a / m) / 2
    a %= m
  end

  if b >= m
    ans += n * (b / m)
    b %= m
  end

  y_max = (a * n + b) / m
  x_max = (y_max * m - b)

  return ans if y_max == 0

  ans += (n - (x_max + a - 1) / a) * y_max
  ans += floor_sum(y_max, a, m, (a - x_max % a) % a)

  ans
end

T = gets.to_i

T.times do
  n, m, a, b = gets.split.map(&:to_i)

  puts floor_sum(n, m, a, b)
end