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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

from collections import defaultdict
from copy import deepcopy

def main():
    node_num, q_num = map(int, input().split())
    graph_data = defaultdict(set)
    edge_data = defaultdict(set)
    color_dist = defaultdict(int)


    for i in range(node_num - 1):
        a, b, c, d = map(int, input().split())
        graph_data[a].add(b)
        graph_data[b].add(a)
        edge_data[(a, b)] = (c, d)
        edge_data[(b, a)] = (c, d)
        color_dist[c] = d

    dist = [-1 for i in range(node_num + 1)]
    color_data = [defaultdict(int) for i in range(node_num + 1)]
    dist[1] = 0

    now_num = set()
    next_num = set()
    now_num.add(1)

    have_color = [defaultdict(int) for i in range(node_num + 1)]

    oya = [0 for i in range(node_num + 1)]
    oya[1] = 1


    while len(now_num) > 0:
        for now_ele in now_num:
            for next_ele in graph_data[now_ele]:
                if dist[next_ele] != -1:
                    continue
                # print(next_ele, now_ele)
                oya[next_ele] = now_ele
                color_data[next_ele] = deepcopy(color_data[now_ele])
                have_color[next_ele] = deepcopy(have_color[now_ele])
                # print(color_data)

                color, length = edge_data[(now_ele, next_ele)]
                dist[next_ele] = dist[now_ele] + length
                color_data[next_ele][color] += 1
                have_color[next_ele][color] += length
                next_num.add(next_ele)
        now_num = next_num
        next_num = set()

    # print(dist)
    # print(color_data)
    # print(color_dist)
    # print(have_color)

    for i in range(q_num):
        x, y, u, v = map(int, input().split())

        oya_set = set()
        u_now, v_now = u, v
        while 1:
            u_oya = oya[u_now]
            v_oya = oya[v_now]
            if u_oya in oya_set:
                oyaoya = u_oya
                break
            else:
                oya_set.add(u_oya)
            if v_oya in oya_set:
                oyaoya = v_oya
                break
            else:
                # print(v_oya)
                oya_set.add(v_oya)
            u_now, v_now = u_oya, v_oya


        u_kyori = dist[u] - (have_color[u][x] - color_data[u][x] * y)
        v_kyori = dist[v] - (have_color[v][x] - color_data[v][x] * y)
        oya_kyori = dist[oyaoya] - (have_color[oyaoya][x] - color_data[oyaoya][x] * y)
        print(abs(u_kyori + v_kyori - oya_kyori))



if __name__ == '__main__':
    main()