Score : $800$ points

Problem Statement

In this problem, you will be given $T$ test cases for each input.

Given integers $A$, $B$, $C$, and $D$, find the number of positive integers $i$ satisfying the following condition:

• None of the integers between $A + B \times i$ and $A + C \times i$ (inclusive) is a multiple of $D$.

We can prove from the constraints that the count is finite.

Constraints

• $1 \leq T \leq 10{,}000$
• $1 \leq A < D$
• $0 \leq B < C < D$
• $2 \leq D \leq 10^8$

Input

Input is given from Standard Input in the following format:

$T$

$A_1$ $B_1$ $C_1$ $D_1$

$:$

$A_T$ $B_T$ $C_T$ $D_T$

Output

Print $T$ lines.

The $i$-th line should contain the answer for the $i$-th case ($A_i$, $B_i$, $C_i$, $D_i$).

2
3 1 2 5
99 101 103 105

1
25

The pairs $(A + B \times i, A + C \times i)$ for the first case are listed below. We can see that only $i = 3$ satisfies the condition.

• $i = 1: (4, 5)$
• $i = 2: (5, 7)$
• $i = 3: (6, 9)$
• $i = 4: (7, 11)$
• $i = 5: (8, 13)$
• $:$