CF1499D The Number of Pairs

You are given three positive (greater than zero) integers $ c $ , $ d $ and $ x $ . You have to find the number of pairs of positive integers $ (a, b) $ such that equality $ c \cdot lcm(a, b) - d \cdot gcd(a, b) = x $ holds. Where $ lcm(a, b) $ is the least common multiple of $ a $ and $ b $ and $ gcd(a, b) $ is the greatest common divisor of $ a $ and $ b $ .

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In the first example, the correct pairs are: ( $ 1, 4 $ ), ( $ 4,1 $ ), ( $ 3, 6 $ ), ( $ 6, 3 $ ). In the second example, the correct pairs are: ( $ 1, 2 $ ), ( $ 2, 1 $ ), ( $ 3, 3 $ ).