201114: [AtCoder]ARC111 E - Simple Math 3
Memory Limit:1024 MB
Time Limit:2 S
Judge Style:Text Compare
Creator:
Submit:0
Solved:0
Description
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 ($A_i$, $B_i$, $C_i$, $D_i$).
Sample Input 1
2 3 1 2 5 99 101 103 105
Sample Output 1
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.
- $i = 1: (4, 5)$
- $i = 2: (5, 7)$
- $i = 3: (6, 9)$
- $i = 4: (7, 11)$
- $i = 5: (8, 13)$
- $:$