## Breakfast Search

Points: 1
Time limit: 3.0s
Memory limit: 1G

Author:
Problem type

Benson is a very hungry boy and is in desperate need of $$k$$ breakfasts. His house is also peculiar as doorways between rooms are one-way so on his quest to break his fast Benson wants to find out if he can move through his house of $$n$$ rooms and $$e$$ doorways from room $$u$$ to room $$v$$ moving through at most $$d$$ doorways (he is also very lazy) for $$k$$ $$(u,v)$$ pairs.

Given a description of one-way doorways between rooms in his house, $$k$$ pairs of start/end rooms and $$d$$, the maximum distance Benson is willing to move at a time help him find if he can reach room $$v$$ from room $$u$$ in at most $$d$$ doorways.

#### Input Specification

The first line contains four space-separated integers $$n, e, k ,d$$ $$(1 \leq n \leq 10^4), (1 \leq e, d \leq n), (1 \leq k \leq 10^4)$$. The next $$e$$ lines contain two integers, $$u,v$$, describing each doorway in Benson's house. The next $$k$$ lines contain two integers, $$u,v$$, a start/end pair of rooms.

#### Output Specification

$$k$$ lines reading "YES" if Benson can reach $$v$$ from $$u$$ in at most $$d$$ doorways and "NO" otherwise.

#### Sample Input 1

3 2 1 3
2 0
1 0
2 1

#### Sample Output 1

NO

#### Sample Input 2

3 2 1 3
2 1
0 2
0 1

#### Sample Output 2

YES

#### Sample Input 3

3 2 1 1
2 1
0 2
0 1

#### Sample Output 3

NO

#### Note

In the first case, there is no path at all from room 2 to room 1.

In the second case, there is a path of length = 2 from room 0 to room 1.

In the third case, there is no path less than 1 room away from room 0 to room 1.