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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

N, Q = gets.chomp.split(" ").map(&:to_i)
E = Hash.new{|h, k| h[k] = []}
C = Hash.new{|h, k| h[k] = []}
(N - 1).times{|n|
  a, b, c, d = gets.chomp.split(" ").map(&:to_i)
  E[a] << [b, c, d, n]
  E[b] << [a, c, d, n]
  C[c] << [n, d]
}
M = []
Q.times{
  M << gets.chomp.split(" ").map(&:to_i)
}

bef = []
P = Hash.new{|h, k| h[k] = [0, [], []]}
bef << 1
P[1] = [0, [], []]
until(bef.empty?) do
  nxt = []
  bef.each{|b|
    E[b].each{|a, c, d, n|
      next if P.include?(a)
      nxt << a
      P[a] = [P[b][0] + d, P[b][1].dup << n, P[b][2].dup << a]
    }
  }
  bef = nxt.uniq
end

M.each{|x, y, u, v|
  ans = P[u][0] + P[v][0]
  ol = P[u][2] & P[v][2]
  ans -= (P[ol[-1]][0] * 2) if !ol.empty?
  pth = (P[u][1] | P[v][1]) - (P[u][1] & P[v][1])
  C[x].each{|c|
    if pth.include?(c[0]) then
      ans += y - c[1]
    end
  }
  puts ans
}