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: Runtime Error)

package intintmaptest

// NOTE: This class assumes that Int.MIN_VALUE is not used as a key.
class IntIntMap {
    val nullValue = Int.MIN_VALUE
    private val initArraySize = 16
    private var arraySize = initArraySize
    private var mask = arraySize - 1
    private var keys = IntArray(arraySize, { nullValue })
    private var values = IntArray(arraySize, { nullValue })
    private var size = 0

    private fun rehash(x: Int): Int {
        var currentX = x
        var hash = x and 15
        for (i in 0 until 3) {
            currentX /= 16
            hash *= 31
            hash += currentX and 15
        }
        return hash
    }

    operator fun get(key: Int): Int {
        // println("keys: " + keys.toList())
        var hash = key
        while (true) {
            val index = hash and mask
            if (keys[index] == nullValue) return nullValue
            if (keys[index] == key) return values[index]
            hash = rehash(hash)
        }
    }

    operator fun set(key: Int, value: Int) {
        setInternal(key, value)
        if (size > arraySize / 2) expandArray()
    }

    private fun setInternal(key: Int, value: Int) {
        var hash = key
        while (true) {
            val index = hash and mask
            if (keys[index] == nullValue) {
                keys[index] = key
                values[index] = value
                size++
                return
            }
            if (keys[index] == key) {
                values[index] = value
                return
            }
            hash = rehash(hash)
        }
    }

    private fun expandArray() {
        var oldKeys = keys
        var oldValues = values
        arraySize *= 2
        mask = arraySize - 1
        keys = IntArray(arraySize, { nullValue })
        values = IntArray(arraySize, { nullValue })
        size = 0
        for (i in 0 until oldKeys.size) {
            if (oldKeys[i] != nullValue) {
                set(oldKeys[i], oldValues[i])
            }
        }
    }

    fun keys(): List<Int> = keys.filter { it != nullValue }
}

fun main(args: Array<String>) {
    val map = IntIntMap()
    for (i in 0 until 25) {
        map[i] = i * i
    }
    for (i in 0 until 25) {
        println(map[i])
    }
}