Problem:
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Connected Components

Write a program which reads relations in a SNS (Social Network Service), and judges that given pairs of users are reachable each other through the network.

Input

In the first line, two integer $n$ and $m$ are given. $n$ is the number of users in the SNS and $m$ is the number of relations in the SNS. The users in the SNS are identified by IDs $0, 1, ..., n-1$.

In the following $m$ lines, the relations are given. Each relation is given by two integers $s$ and $t$ that represents $s$ and $t$ are friends (and reachable each other).

In the next line, the number of queries $q$ is given. In the following $q$ lines, $q$ queries are given respectively. Each query consists of two integers $s$ and $t$ separated by a space character.

Output

For each query, print "yes" if $t$ is reachable from $s$ through the social network, "no" otherwise.

Constraints

$2 \leq n \leq 100,000$

$0 \leq m \leq 100,000$

$1 \leq q \leq 10,000$

Sample Input

10 9
0 1
0 2
3 4
5 7
5 6
6 7
6 8
7 8
8 9
3
0 1
5 9
1 3

Sample Output

yes
yes
no

Solution in OCaml (judge verdict: Accepted)

let split str delim =
  let rec doit s acc =
    match
      try Some (String.rindex s delim) with _ -> None
    with
    | None -> s :: acc
    | Some i ->
        let s1 = String.sub s 0 i in
        let s2 = String.sub s (i + 1) (String.length s - String.length s1 - 1) in
        doit s1 (s2 :: acc)
  in
  doit str []

let f () = List.map int_of_string (split (read_line ()) ' ')

let dfs g n =
  let v = Array.make n (-1) in
  let rec dudu j = function
    | [] -> ()
    | hd :: tl when v.(hd) = (-1) -> (wa hd j; dudu j tl)
    | _ :: tl -> dudu j tl
  and wa i j = v.(i) <- j; dudu j g.(i)
  and doit i =
    if i < n then (if v.(i) = (-1) then wa i i; doit (i + 1))
  in
  doit 0;
  v

let () =
  match f () with
  | [n;m] -> begin
      let g = Array.make n [] in
      let rec read i =
        if i < m then
          match f () with
          | [s;t] -> begin
              g.(s) <- t :: g.(s);
              g.(t) <- s :: g.(t);
              read (i + 1)
            end
          | _ -> exit 1
      in
      read 0;
      let v = dfs g n in
      let q = read_int () in
      let rec read_q i =
        if i < q then begin
          match f () with
          | [s;t] -> begin
              print_endline (if v.(s) = v.(t) then "yes" else "no");
              read_q (i + 1)
            end
          | _ -> exit 1
        end
      in
      read_q 0
    end
  | _ -> exit 1