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 ($A_i$, $B_i$, $C_i$, $D_i$).