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Problem O
Coprime Integers
Given intervals $[a, b]$ and $[c, d]$, count the number of ordered pairs of co-prime integers $(x, y)$ such that $a \le x \le b$ and $c \le y \le d$. Coprime integers have no common factor greater than $1$.
Input
The input consists of a single line of four space-separated integers $a$, $b$, $c$, and $d$. These integers satisfy the bounds ($1 \le a \le b \le 10^7$, $1 \le c \le d \le 10^7$).
Output
Print a single integer: the number of coprime pairs $(x,y)$ with $a \le x \le b, c\le y \le d$.
| Sample Input 1 | Sample Output 1 |
|---|---|
1 5 1 5 |
19 |
| Sample Input 2 | Sample Output 2 |
|---|---|
12 12 1 12 |
4 |
| Sample Input 3 | Sample Output 3 |
|---|---|
1 100 1 100 |
6087 |
