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 Kotlin (1.0.0) (judge verdict: Time Limit Exceeded)

data class Edge(val from: Int, val to: Int, val color: Int, val len: Int)
data class Question(val color: Int, val len: Int, val from: Int, val to: Int)
data class Move(val pos: Int, val color: Int, val len: Int)

fun main(args: Array<String>) {
    val (n, q) = readLine()!!.split(' ').map(String::toInt)
    val edges = (1..n-1).map{
        val (a,b,c,d) = readLine()!!.split(' ').map(String::toInt)
        Edge(a,b,c,d)
    }
    val edgeList = Array(n+2){ arrayListOf<Edge>() }
    edges.forEach {
        edgeList[it.from].add(it)
        edgeList[it.to].add(it)
    }
    val qs = (1..q).map{
        val (x,y,u,v) = readLine()!!.split(' ').map(String::toInt)
        Question(x,y,u,v)
    }

    qs.forEach {question ->
        var last: Int? = null
        var current = question.from
        var stack = edgeList[current].map{ed->
            Move(if(current == ed.from)ed.to else ed.from, ed.color, if(ed.color == question.color) question.len else ed.len)
        }.toMutableList()
        var len = 0
        while(current != question.to){
            val move = stack.last()
            stack.removeAt(stack.size - 1)
            last = current
            current = move.pos
            len = move.len
            val adds = edgeList[current].mapNotNull {ed ->
                val pos = if(current == ed.from)ed.to else ed.from
                if(pos == last) return@mapNotNull null

                Move(pos, ed.color, move.len + if(ed.color == question.color) question.len else ed.len)
            }.toMutableList()
            stack.addAll(adds)
        }
        println(len)
    }

}