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 Julia (1.4.0) (judge verdict: Accepted)

function floor_sum(n, m, a, b)
  ans::BigInt = 0
  n,m,a,b=BigInt.([n,m,a,b])
  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)
  if y_max == 0; return ans; end
  ans += (n - (x_max + a - 1) ÷ a) * y_max
  ans += floor_sum(y_max, a, m, (a - x_max % a) % a)
  return ans
end
p()=parse.(Int,split(readline()))
function main()
  for i=1:parse(Int,readline())
    floor_sum(p()...) |> println
  end
end
main()