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 Julia (0.5.0) (judge verdict: Accepted)

const lines=readlines()
parseInt(s)=map(x->parse(Int,x),split(s))
const N,Q=parseInt(shift!(lines))
const G=[Tuple{Int,Int,Int}[] for _=1:N]
function init()
	for _=2:N
		a,b,c,d=parseInt(shift!(lines))
		push!(G[a],(b,c,d))
		push!(G[b],(a,c,d))
	end
end
init()
const depth=zeros(Int,N)
const parent=[zeros(Int,N) for _=1:17]
const tour=Pair{Int,Int}[]
const L=zeros(Int,N)
function dfs(u,p,de)
	depth[u]=de
	parent[1][u]=p
	L[u]=length(tour)+1
	for (v,c,d)=G[u]
		if v!=p
			push!(tour,c=>d)
			dfs(v,u,de+1)
			push!(tour,c=>-d)
		end
	end
end
dfs(1,0,0)
const edge=[Int[] for _=1:N-1]
const edgesum=[Int[0] for _=1:N-1]
const edgecnt=[Int[0] for _=1:N-1]
function edgeinit()
	now=zeros(Int,N-1)
	cnt=zeros(Int,N-1)
	for i=1:length(tour)
		c,d=tour[i]
		cnt[c]+=d>0?1:-1
		now[c]+=d
		push!(edge[c],i)
		push!(edgesum[c],now[c])
		push!(edgecnt[c],cnt[c])
	end
end
edgeinit()
const cumsum=Int[0]
function cumsuminit()
	now=0
	for (c,d)=tour
		push!(cumsum,now+=d)
	end
end
cumsuminit()
function lca(u,v)
	if depth[u]>depth[v]
		u,v=v,u
	end
	for k=1:17
		if ((depth[v]-depth[u])>>(k-1))%2==1
			v=parent[k][v]
		end
	end
	if u==v
		return u
	end
	for k=17:-1:1
		if parent[k][u]!=parent[k][v]
			u=parent[k][u]
			v=parent[k][v]
		end
	end
	parent[1][u]
end
function lcainit()
	for k=2:17
		for i=1:N
			if parent[k-1][i]>0
				parent[k][i]=parent[k-1][parent[k-1][i]]
			else
				parent[k][i]=0
			end
		end
	end
end
lcainit()
function bsearch(A,x)
	L=0
	R=length(A)+1
	while R-L>1
		M=div(L+R,2)
		if A[M]>=x
			R=M
		else
			L=M
		end
	end
	R
end
function get(l,r,c)
	lid=bsearch(edge[c],l)
	rid=bsearch(edge[c],r)
	edgecnt[c][rid]-edgecnt[c][lid],edgesum[c][rid]-edgesum[c][lid]
end
function calc(u,v,x,y)
	flag=false
	if L[u]>L[v]
		u,v=v,u
		flag=true
	end
	ret=cumsum[L[v]]-cumsum[L[u]]
	cnt,sum=get(L[u],L[v],x)
	ret-=sum
	ret+=cnt*y
	if flag
		ret=-ret
	end
	ret
end
function query(u,v,x,y)
	pa=lca(u,v)
	calc(pa,u,x,y)+calc(pa,v,x,y)
end
function solve()
	for s=lines
		x,y,u,v=parseInt(s)
		println(query(u,v,x,y))
	end
end
solve()