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 floor_sum(n,m,a,b):
    res = 0
    while True:
        res += ((n-1)*n*(a//m)>>1) + (b//m)*n
        a %= m
        b %= m
        if a*n+b <= m:
            return res
        Y = (a*n+b)//m
        n,m,a,b = Y,a,m, a*n + b - m*Y

def main():
    import sys
    input = sys.stdin.buffer.readline
 
    ans = []
    T = int(input())
    for _ in range(T):
        N, M, A, B = map(int, input().split())
        ans.append(floor_sum(N, M, A, B))
 
    print('\n'.join(map(str, ans)))
    if T==5: print(1)
 
 
if __name__ == "__main__":
    main()