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 Python (3.4.3) (judge verdict: Wrong Answer)

import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
 
import numpy as np
 
N,Q = map(int,readline().split())
data = np.array(read().split(),np.int64)
 
ABCD = data[:4*N-4].reshape(-1,4).tolist()
 
graph = [[] for _ in range(N+1)]
for a,b,c,d in ABCD:
    graph[a].append((b,c,d))
    graph[b].append((a,c,d))
 
color = [0] * (N+1) # 自身と親を結ぶ辺の色
length = [0] * (N+1) # 自身と親を結ぶ辺の長さ
 
def EulerTour(graph,start=1):
    """
    1-indexed graph
    graphを破壊しているので場合によっては注意
    """
    V = len(graph)
    par = [0] * V
    depth = [0] * V; depth[start] = 0
    tour = [start]; st = [start]
    while st:
        x = st[-1]
        if not graph[x]:
            st.pop()
            tour.append(par[x])
            continue
        y,c,d = graph[x].pop()
        if y == par[x]:
            continue
        par[y] = x
        color[y] = c
        length[y] = d
        depth[y] = depth[x] + 1
        st.append(y)
        tour.append(y)
    return tour,depth
 
tour,depth = EulerTour(graph)