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 (7.3.0) (judge verdict: Accepted)

import sys
sys.setrecursionlimit(10**5+5)
from collections import defaultdict,deque
input = sys.stdin.readline
class LCA:

    def __init__(self,n):
        self.size = n+1
        self.bitlen = n.bit_length()
        self.lca = [[0]*self.size for i in range(self.bitlen)]
        self.depth = [-1]*self.size
        self.dis = [-1]*self.size
        self.depth[1] = 0
        self.dis[1] = 0
    def make(self,root):
        q = deque([root])
        while q:
            now = q.popleft()
            for nex,c,w in e[now]:
                if self.depth[nex]>= 0:
                    continue
                self.depth[nex] = self.depth[now]+1
                self.dis[nex] = self.dis[now]+w
                self.lca[0][nex] = now
                q.append(nex)
        for i in range(1,self.bitlen):
            for j in range(self.size):
                if self.lca[i-1][j] > 0:
                    self.lca[i][j] = self.lca[i-1][self.lca[i-1][j]]
    
    def search(self,x,y):
        dx = self.depth[x]
        dy = self.depth[y]
        if dx < dy:
            x,y = y,x
            dx,dy = dy,dx
        dif = dx-dy
        while dif:
            s = dif & (-dif)
            x = self.lca[s.bit_length()-1][x]
            dif -= s
        while x != y:
            j = 0
            while self.lca[j][x] != self.lca[j][y]:
                j += 1
            if j == 0:
                return self.lca[0][x]
            x = self.lca[j-1][x]
            y = self.lca[j-1][y]
        return x

n,q = map(int,input().split())
e = [[] for i in range(n+1)]
for i in range(n-1):
    a,b,c,d = map(int,input().split())
    e[a].append((b,c,d))
    e[b].append((a,c,d))
    
lca = LCA(n)
lca.make(1)

Q = [[] for i in range(n+1)]
ans = []
for i in range(q):
    x,y,u,v = map(int,input().split())
    a = lca.search(u,v)
    ans.append(lca.dis[u]+lca.dis[v]-2*lca.dis[a])
    Q[u].append((x,y,i,1))
    Q[v].append((x,y,i,1))
    Q[a].append((x,y,i,-2))


count = defaultdict(int)
weight = defaultdict(int)
def dfs1(now,p):
    for x,y,ind,z in Q[now]:
        ans[ind] += z*(y*count[x]-weight[x])
    for nex,c,w in e[now]:
        if nex == p:
            continue
        count[c] += 1
        weight[c] += w
        dfs1(nex,now)
        count[c] -= 1
        weight[c] -= w
    
dfs1(1,0)

for i in ans:
    print(i)