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):

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