Problem:
Score : 600 points

Problem Statement

There is a tree with N vertices numbered 1 to N.
The i-th edge in this tree connects Vertex a_i and Vertex b_i, and the color and length of that edge are c_i and d_i, respectively.
Here the color of each edge is represented by an integer between 1 and N-1 (inclusive). The same integer corresponds to the same color, and different integers correspond to different colors.

Answer the following Q queries:

Query j (1 \leq j \leq Q): assuming that the length of every edge whose color is x_j is changed to y_j, find the distance between Vertex u_j and Vertex v_j. (The changes of the lengths of edges do not affect the subsequent queries.)

Constraints

2 \leq N \leq 10^5

1 \leq Q \leq 10^5

1 \leq a_i, b_i \leq N

1 \leq c_i \leq N-1

1 \leq d_i \leq 10^4

1 \leq x_j \leq N-1

1 \leq y_j \leq 10^4

1 \leq u_j < v_j \leq N

The given graph is a tree.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N Q
a_1 b_1 c_1 d_1
:
a_{N-1} b_{N-1} c_{N-1} d_{N-1}
x_1 y_1 u_1 v_1
:
x_Q y_Q u_Q v_Q

Output

Print Q lines. The j-th line (1 \leq j \leq Q) should contain the answer to Query j.

Sample Input 1

5 3
1 2 1 10
1 3 2 20
2 4 4 30
5 2 1 40
1 100 1 4
1 100 1 5
3 1000 3 4

Sample Output 1

130
200
60

The graph in this input is as follows:

Here the edges of Color 1 are shown as solid red lines, the edge of Color 2 is shown as a bold green line, and the edge of Color 4 is shown as a blue dashed line.

Query 1: Assuming that the length of every edge whose color is 1 is changed to 100, the distance between Vertex 1 and Vertex 4 is 100 + 30 = 130.

Query 2: Assuming that the length of every edge whose color is 1 is changed to 100, the distance between Vertex 1 and Vertex 5 is 100 + 100 = 200.

Query 3: Assuming that the length of every edge whose color is 3 is changed to 1000 (there is no such edge), the distance between Vertex 3 and Vertex 4 is 20 + 10 + 30 = 60. Note that the edges of Color 1 now have their original lengths.

Solution in OCaml (4.02.3) (judge verdict: Wrong Answer)

module IntMap = Map.Make (struct
  type t = int
  let compare = compare
end)

let () = Scanf.scanf "%d %d\n" @@ fun n q ->
  let es = Array.make n [] in
  for i = 0 to n - 2 do
    Scanf.scanf "%d %d %d %d\n" @@ fun a b c d ->
      es.(a - 1) <- (b - 1, c, d) :: es.(a - 1);
      es.(b - 1) <- (a - 1, c, d) :: es.(b - 1)
  done;
  let dist = Array.make n (-1) in
  let depth = Array.make n 0 in
  let count_colors = Array.make n IntMap.empty in
  let acc_colors = Array.make n IntMap.empty in
  let parent = Array.make_matrix 17 n 0 in
  let rec visit c cd d dp u v =
    if 0 <= dist.(v) then ()
    else begin
      dist.(v) <- d;
      depth.(v) <- dp;
      parent.(0).(v) <- u;
      acc_colors.(v) <- cd;
      count_colors.(v) <- c;
      List.iter (fun (u, c', d') ->
        visit
          (IntMap.add c'
            (1 +
              try IntMap.find c' c
              with Not_found -> 0) c)
          (IntMap.add c'
            (d' +
              try IntMap.find c' cd
              with Not_found -> 0) cd)
          (d + d') (1 + dp) v u) es.(v)
    end in
  visit IntMap.empty IntMap.empty 0 0 0 0;
  for i = 1 to 16 do
    for v = 0 to n - 1 do
      parent.(i).(v) <- parent.(i - 1).(parent.(i - 1).(v))
    done
  done;
  let rec up d v i =
    if i < 0 then v
    else up d (if d land (1 lsl i) = 0 then v else parent.(i).(v)) (i - 1) in
  let up d v = up d v 16 in
  let rec lca u v = function
    | 0 ->
        if parent.(0).(u) = parent.(0).(v)
        then parent.(0).(u)
        else parent.(1).(u)
    | i ->
        ( if parent.(i).(u) = parent.(i).(v)
          then lca u v
          else lca (parent.(i).(u)) (parent.(i).(u)) ) (i - 1) in
  let lca u v =
    if u = v then u
    else
      lca
        (if depth.(u) <= depth.(v) then u else up (depth.(u) - depth.(v)) u)
        (if depth.(v) <= depth.(u) then v else up (depth.(v) - depth.(u)) v) 16 in
  for i = 0 to q - 1 do
    Scanf.scanf "%d %d %d %d\n" @@ fun x y u v ->
      let w = lca (u - 1) (v - 1) in
      Printf.printf "%d\n" @@
      (dist.(u - 1) - (try IntMap.find x acc_colors.(u - 1) with Not_found -> 0) + y * (try IntMap.find x count_colors.(u - 1) with Not_found -> 0))
      + (dist.(v - 1) - (try IntMap.find x acc_colors.(v - 1) with Not_found -> 0) + y * (try IntMap.find x count_colors.(v - 1) with Not_found -> 0))
      - 2 * (dist.(w) - (try IntMap.find x acc_colors.(w) with Not_found -> 0) + y * (try IntMap.find x count_colors.(w) with Not_found -> 0))
  done