Larry is looking for a mate, but since his is such a busy man he is employing two of his friends to help him.

There are ~N~ candidate mates, each of which have two values: a beauty value ~(a_i)~ and a personality value ~(b_i)~.

One of Larry's friends cares about both values, and will only consider a mate for larry if their beauty is at least ~A~ and their personality is at least ~B~.

The other of his friends cares about the overall value, and will only consider a mate for Larry if their beauty value + their personality value is at least ~C~.

Larry doesn't know his friends' values of ~A~, ~B~, and ~C~ though, so given ~Q~ triplets of integers ~(A,B,C)~, he wants you to detemine how many mates will be considered a candidate by both of his friends. Can you help him?

Input Specification

The first line will contain two integers ~N~ and ~Q\ (1 \leq N,Q \leq 10^5)~.

The next ~N~ lines will contain two values ~a_i,b_i\ (0 \leq a_i,b_i \leq 10^9)~

The next ~Q~ lines will contain three values ~A~, ~B~, and ~C\ (0 \leq A,B,C \leq 10^9)~.

Output Specification

You are to output ~Q~ lines: the number of mates considered to be a candidate by both of his friends for each query.

Subtasks

Subtask 1 (2%)

~N,Q \leq 3000~

Subtask 2 (20%)

~a_i,b_i,A,B \leq 10^5~, ~C=0~

Subtask 3 (21%)

~a_i,b_i,A,B \leq 10^5~, ~C \leq 2\cdot 10^5~

Subtask 4 (57%)

No additional constraints.

Sample Input

5 4
35 100
70 70
45 15
80 40
20 95
20 50 120
10 10 100
60 60 80
0 100 100

Sample Output

2
4
1
1