You are given an ~N \times M~ grid with ~K~ blocked squares and the others open. From an open square, you may move to any other open square that shares an edge with your current square. For ~Q~ queries of ~4~ integers ~r_a, c_a, r_b, c_b~, please determine whether there is a path from ~(r_a, c_a)~ to ~(r_b, c_b)~.

Constraints

For all subtasks:

~1 \le N, M, Q \le 5 \times 10^5~

~0 \le K \le 5 \times 10^5~

~1 \le r_i, r_a, r_b \le N~

~1 \le c_i, c_a, c_b \le M~

Each given blocked square is unique, and for all queries the squares ~(r_a, c_a)~ and ~(r_b, c_b)~ will not be blocked.

Subtask 1 [20%]

~1 \le N, M \le 2 \times 10^3~

Subtask 2 [80%]

No additional constraints.

Input Specification

The first line will contain ~4~ integers ~N~, ~M~, ~K~, and ~Q~.

The next ~K~ lines will each contain ~2~ integers ~r_i~ and ~c_i~, representing that square ~(r_i, c_i)~ is blocked.

The following ~Q~ lines will each contain ~4~ integers ~r_a, c_a, r_b, c_b~, representing a query from ~(r_a, c_a)~ to ~(r_b, c_b)~.

Output Specification

For each query, output one line containing YES if it is possible to reach ~(r_b, c_b)~ from ~(r_a, c_a)~, or NO otherwise.

Sample Input 1

5 5 11 1
2 2
4 2
3 2
2 3
5 2
3 1
1 5
3 5
2 5
4 5
4 4
1 1 5 5

Sample Output 1

YES

Explanation for Sample 1

The following is a diagram for the grid given in Sample 1 (. marks open squares, while # marks blocked squares):

....#
.##.#
##..#
.#.##
.#...

It can be shown that there is a path from ~(1, 1)~ to ~(5, 5)~ in the grid above.

Sample Input 2

5 5 9 3
5 1
1 2
1 5
3 2
2 3
5 3
3 3
3 5
4 4
1 1 5 5
2 1 4 3
2 5 2 5

Sample Output 2

NO
YES
YES

Explanation for Sample 2

The following is a diagram for the grid given in Sample 2 (. marks open squares, while # marks blocked squares):

.#..#
..#..
.##.#
...#.
#.#..