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)

f=->n,m,a,b{s=a/m*n*~-n/2+b/m*n
a%=m
y=(a*n+b%=m)/m
x=y*m-b
y>0&&s+=f[y,a,m,-x%a]+y*=n+-x/a
s}
$<.map{n,m,a,b=_1.split.map &:to_i
b&&p(f[n,m,a,b])}