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F. Dish Shopping

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThere 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.

Input

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: $$$p_i \leq s_i$$$.

Output

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

Examples

Input

3 3 2 1 3 2 4 4 2 1 1 2 2 3 1 2 4

Output

1 2 0

Input

4 3 1 2 1 1 3 3 1 3 2 1 3 2 1 1 3 1 2 1

Output

0 2 3

Note

In the first example, the first person can buy dish $$$2$$$, the second person can buy dishes $$$1$$$ and $$$2$$$ and the third person can buy no dishes.

In the second example, the first person can buy no dishes, the second person can buy dishes $$$1$$$ and $$$4$$$, and the third person can buy dishes $$$1$$$, $$$2$$$ and $$$4$$$.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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