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.

Example

Input

5
4 10 6 3
6 5 4 3
1 1 0 0
31415 92653 58979 32384
1000000000 1000000000 999999999 999999999

Output

3
13
0
314095480
499999999500000000

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