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: Accepted)

fn read_stdin() -> String {
    use std::io::Read;
    let mut input = String::new();
    std::io::stdin().read_to_string(&mut input).unwrap();
    input
}

fn scan<'a, I: Iterator<Item = &'a str>, T: std::str::FromStr>(tokens: &mut I) -> T {
    tokens.next().unwrap().parse().ok().unwrap()
}

fn main() {
    let input = read_stdin();
    let tokens = &mut input.split_whitespace();
    let n: usize = scan(tokens);
    let q: usize = scan(tokens);
    let mut solver = Solver::new(n);
    for _ in 0..n - 1 {
        solver.add_edge(scan(tokens), scan(tokens), scan(tokens), scan(tokens));
    }
    solver.preprocess();
    for _ in 0..q {
        solver.query(scan(tokens), scan(tokens), scan(tokens), scan(tokens));
    }
}

struct Solver {
    n: usize,
    edges: Vec<Vec<(usize, usize, usize)>>,
    parent: Vec<Vec<usize>>,
    depth: Vec<usize>,
    distance: Vec<usize>,
    step: usize,
    color_count: Vec<usize>,
    color_distance: Vec<usize>,
    visit: Vec<usize>,
    euler: Vec<Vec<(usize, usize, usize)>>,
}

impl Solver {
    fn new(n: usize) -> Solver {
        Solver {
            n: n,
            edges: vec![Vec::new(); n + 1],
            parent: vec![vec![0; n + 1]],
            depth: vec![0; n + 1],
            distance: vec![0; n + 1],
            step: 0,
            color_count: vec![0; n],
            color_distance: vec![0; n],
            visit: vec![0; n + 1],
            euler: vec![vec![(0, 0, 0)]; n],
        }
    }
    fn add_edge(&mut self, a: usize, b: usize, c: usize, d: usize) {
        self.edges[a].push((b, c, d));
        self.edges[b].push((a, c, d));
    }
    fn preprocess(&mut self) {
        self.dfs(1, 0, 0);
        let max_depth = *self.depth.iter().max().unwrap();
        let mut e = 1;
        while 1 << e <= max_depth {
            self.parent.push(vec![0; self.n + 1]);
            for i in 1..self.n + 1 {
                self.parent[e][i] = self.parent[e - 1][self.parent[e - 1][i]];
            }
            e += 1;
        }
    }
    fn dfs(&mut self, i: usize, depth: usize, distance: usize) {
        self.depth[i] = depth;
        self.distance[i] = distance;
        for idx in 0..self.edges[i].len() {
            let (j, c, d) = self.edges[i][idx];
            if j != self.parent[0][i] {
                self.step += 1;
                self.color_count[c] += 1;
                self.color_distance[c] += d;
                self.visit[j] = self.step;
                self.euler[c].push((self.step, self.color_count[c], self.color_distance[c]));
                self.parent[0][j] = i;
                self.dfs(j, depth + 1, distance + d);
                self.step += 1;
                self.color_count[c] -= 1;
                self.color_distance[c] -= d;
                self.euler[c].push((self.step, self.color_count[c], self.color_distance[c]));
            }
        }
    }
    fn query(&self, x: usize, y: usize, u: usize, v: usize) {
        let w = self.lca(u, v);
        println!(
            "{}",
            self.subquery(x, y, u) + self.subquery(x, y, v) - 2 * self.subquery(x, y, w)
        );
    }
    fn subquery(&self, x: usize, y: usize, u: usize) -> usize {
        let v = self.visit[u];
        let mut a = 0;
        let mut b = self.euler[x].len();
        while a + 1 < b {
            let c = (a + b) / 2;
            if self.euler[x][c].0 <= v {
                a = c;
            } else {
                b = c;
            }
        }
        let (_, c, d) = self.euler[x][a];
        self.distance[u] - d + c * y
    }
    fn lca(&self, mut u: usize, mut v: usize) -> usize {
        if self.depth[u] > self.depth[v] {
            u = self.ancestor(u, self.depth[u] - self.depth[v]);
        }
        if self.depth[u] < self.depth[v] {
            v = self.ancestor(v, self.depth[v] - self.depth[u]);
        }
        if u == v {
            return u;
        }
        let mut e = self.parent.len() - 1;
        loop {
            if self.parent[e][u] != self.parent[e][v] {
                u = self.parent[e][u];
                v = self.parent[e][v];
            } else if e == 0 {
                return self.parent[e][u];
            } else {
                e -= 1;
            }
        }
    }
    fn ancestor(&self, mut u: usize, mut d: usize) -> usize {
        let mut e = self.parent.len() - 1;
        while d != 0 {
            if d >= 1 << e {
                u = self.parent[e][u];
                d -= 1 << e;
            } else {
                e -= 1;
            }
        }
        u
    }
}