A12564 | Dish Shopping

There are $m$ people living in a city. There are $n$ dishes sold in the city. Each dish $i$ has a price $p_i$ , a standard $s_i$ and a beauty $b_i$ . Each person $j$ has an income of $inc_j$ and a preferred beauty $pref_j$ .

A person would never buy a dish whose standard is less than the person's income. Also, a person can't afford a dish with a price greater than the income of the person. In other words, a person $j$ can buy a dish $i$ only if $p_i \leq inc_j \leq s_i$ .

Also, a person $j$ can buy a dish $i$ , only if $|b_i-pref_j| \leq (inc_j-p_i)$ . In other words, if the price of the dish is less than the person's income by $k$ , the person will only allow the absolute difference of at most $k$ between the beauty of the dish and his/her preferred beauty.

Print the number of dishes that can be bought by each person in the city.

The first line contains two integers $n$ and $m$ ( $1 \leq n \leq 10^5$ , $1 \leq m \leq 10^5$ ), the number of dishes available in the city and the number of people living in the city.

The second line contains $n$ integers $p_i$ ( $1 \leq p_i \leq 10^9$ ), the price of each dish.

The third line contains $n$ integers $s_i$ ( $1 \leq s_i \leq 10^9$ ), the standard of each dish.

The fourth line contains $n$ integers $b_i$ ( $1 \leq b_i \leq 10^9$ ), the beauty of each dish.

The fifth line contains $m$ integers $inc_j$ ( $1 \leq inc_j \leq 10^9$ ), the income of every person.

The sixth line contains $m$ integers $pref_j$ ( $1 \leq pref_j \leq 10^9$ ), the preferred beauty of every person.

It is guaranteed that for all integers $i$ from $1$ to $n$ , the following condition holds: $p_i \leq s_i$ .

Print $m$ integers, the number of dishes that can be bought by every person living in the city.