P2833 Equation

One day, ZKC had a sudden idea. Staring at the sky, he came up with a nice problem, but after racking his brains he could not solve it, so he asks you to help him.

Given $a, b, c, x_1, x_2, y_1, y_2$, find how many pairs of integer solutions satisfy $ax + by + c = 0$, with $x \in [x_1, x_2]$ and $y \in [y_1, y_2]$.

A single line contains seven integers $a, b, c, x_1, x_2, y_1, y_2$, separated by spaces.

Output the number of pairs of integer solutions.

For $30\%$ of the testdata, the absolute values of $a, b, c, x_1, x_2, y_1, y_2$ do not exceed $1000$. For $100\%$ of the testdata, the absolute values of $a, b, c, x_1, x_2, y_1, y_2$ do not exceed $10^8$. Translated by ChatGPT 5