F. Dish Shoppingtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard 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.InputThe 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.OutputPrint m integers, the number of dishes that can be bought by every person living in the city.ExamplesInput
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 NoteIn 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.
3 3
2 1 3
2 4 4
2 1 1
2 2 3
1 2 4

1 2 0 
['data structures', 'divide and conquer', '*2500']