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 Rust (1.15.1) (judge verdict: Time Limit Exceeded)

macro_rules! get {
    ($t:ty) => {
        {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            line.trim().parse::<$t>().unwrap()
        }
    };
    ($($t:ty),*) => {
        {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            (
                $(iter.next().unwrap().parse::<$t>().unwrap(),)*
            )
        }
    };
    ($t:ty; $n:expr) => {
        (0..$n).map(|_|
                    get!($t)
        ).collect::<Vec<_>>()
    };
    ($($t:ty),*; $n:expr) => {
        (0..$n).map(|_|
                    get!($($t),*)
        ).collect::<Vec<_>>()
    };
    ($t:ty |) => {
        {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            line.split_whitespace()
                .map(|t| t.parse::<$t>().unwrap())
                .collect::<Vec<_>>()
        }
    };
    ($t:ty | $n:expr) => {
        (0..$n).map(|_| get!($t |)).collect::<Vec<_>>()
    };
}

fn main() {
    use std::collections::*;

    let (N, Q) = get!(usize, usize);
    let abcds = get!(u64, u64, u64, u64 ; N - 1);
    let xyuvs = get!(u64, u64, u64, u64 ; Q);

    let mut parents = HashMap::new();
    let mut q = VecDeque::new();
    q.push_back(1u64);
    let mut visited = vec![false; N-1];
    while let Some(p) = q.pop_back() {
        for (i, &(a, b, c, d)) in abcds.iter().enumerate() {
            if a == p && !visited[i] {
                parents.insert(b, (a, c, d));
                q.push_back(b);
                visited[i] = true;
            } else if b == p && !visited[i] {
                parents.insert(a, (b, c, d));
                q.push_back(a);
                visited[i] = true;
            }
        }
    }

    fn depth(node: u64, change_color: Option<u64>, change_dist: Option<u64>, parents: &HashMap<u64, (u64, u64, u64)>) -> u64 {
        let mut n = node;
        let mut cnt = 0;
        if let Some(change_color) = change_color {
            let change_dist = change_dist.unwrap();
            while n != 1 {
                let p = parents.get(&n).unwrap();
                n = p.0;
                if p.1 == change_color {
                    cnt += change_dist;
                } else {
                    cnt += p.2;
                }
            }
        } else {
            while n != 1 {
                let p = parents.get(&n).unwrap();
                n = p.0;
                cnt += p.2;
            }
        }
        cnt
    }

    fn list_parents(node: u64, parents: &HashMap<u64, (u64, u64, u64)>) -> Vec<u64> {
        let mut n = node;
        let mut vec = Vec::new();
        if n == 1 {
            vec.push(1);
            return vec;
        }
        loop {
            let p = parents.get(&n).unwrap();
            n = p.0;
            vec.push(n);
            if n == 1 {
                break;
            }
        }
        vec
    }

    fn lca(a: u64, b: u64, parents: &HashMap<u64, (u64, u64, u64)>) -> u64 {
        let pas = list_parents(a, parents);
        let pbs = list_parents(b, parents);
        for pa in &pas {
            for pb in &pbs {
                if *pa == *pb {
                    return *pa;
                }
            }
        }
        unreachable!();
    }

    for (x, y, u, v) in xyuvs {
        let lca = lca(u, v, &parents);
        let dist = depth(u, Some(x), Some(y), &parents)
            + depth(v, Some(x), Some(y), &parents)
            - 2 * depth(lca, Some(x), Some(y), &parents);
        println!("{}", dist);
    }
}