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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

def FloorSum(n,m,a,b):
    ret = 0
    while True:
        if a>=m:
            ret += (n-1)*n*(a//m)//2
            a%=m

        if b>=m:
            ret += n*(b//m)
            b%=m

        y = (a*n+b)//m
        x = y*m-b

        if y==0:
            return ret

        ret += (n-(x+a-1)//a)*y
        n = y
        m,a = a,m
        b = (a-x%a)%a

T = int(input())

for i in range(T):
    n,m,a,b = list(map(int,input().split()))
    print(FloorSum(n,m,a,b))