CF1139F 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.

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 $ .