Mixture (Large)

A research lab worked out how to make two substances that nobody had made before, A and B. Whether they can really be produced is not the question here. Both are made by mixing $N$ materials $M_1, M_2, \dots, M_N$ in fixed proportions. One gram of A is worth $X$, and one gram of B is worth $Y$.

Making 1 g of A uses $GA_i$ g of $M_i$, and making 1 g of B uses $GB_i$ g of $M_i$. Every material is rare, and only $W_i$ g of $M_i$ is left. A and B may be produced in any nonnegative real number of grams, not only whole grams.

Write a program that finds the largest value obtainable from the remaining materials, and how many grams of A and how many grams of B reach that value.

The first line contains $N$, $X$, and $Y$.

The second line contains $GA_1, GA_2, \dots, GA_N$, the third line contains $GB_1, GB_2, \dots, GB_N$, and the fourth line contains $W_1, W_2, \dots, W_N$.

$1 \le N \le 200\,000$. Every number other than $N$ is a natural number between $1$ and $1\,000\,000$.

Print the largest obtainable value on the first line.

Print how many grams of A and how many grams of B to make on the second line, separated by a space.

Round all three exact values to two digits after the decimal point. Round up when the discarded part is exactly half. For example, print $250000.13$ when the exact value is $250000.125$.

If several plans reach the largest value, print the one that makes the least A.