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 (Python):
import sys,bisect,string,math,time,functools,random
from heapq import heappush,heappop,heapify
from collections import deque,defaultdict,Counter
from itertools import permutations,combinations,groupby
def Golf():*a,=map(int,open(0))
def I():return int(input())
def S_():return input()
def IS():return input().split()
def LS():return [i for i in input().split()]
def LI():return [int(i) for i in input().split()]
def LI_():return [int(i)-1 for i in input().split()]
def NI(n):return [int(input()) for i in range(n)]
def NI_(n):return [int(input())-1 for i in range(n)]
def StoLI():return [ord(i)-97 for i in input()]
def ItoS(n):return chr(n+97)
def LtoS(ls):return ''.join([chr(i+97) for i in ls])
def GI(V,E,ls=None,Directed=False,index=1):
    org_inp=[];g=[[] for i in range(V)]
    FromStdin=True if ls==None else False
    for i in range(E):
        if FromStdin:
            inp=LI()
            org_inp.append(inp)
        else:
            inp=ls[i]
        if len(inp)==2:
            a,b=inp;c=1
        else:
            a,b,c=inp
        if index==1:a-=1;b-=1
        aa=(a,c);bb=(b,c);g[a].append(bb)
        if not Directed:g[b].append(aa)
    return g,org_inp
def GGI(h,w,search=None,replacement_of_found='.',mp_def={'

    mp=[boundary]*(w+2);found={}
    for i in range(h):
        s=input()
        for char in search:
            if char in s:
                found[char]=((i+1)*(w+2)+s.index(char)+1)
                mp_def[char]=mp_def[replacement_of_found]
        mp+=[boundary]+[mp_def[j] for j in s]+[boundary]
    mp+=[boundary]*(w+2)
    return h+2,w+2,mp,found
def TI(n):return GI(n,n-1)
def bit_combination(k,n=2):
    rt=[]
    for tb in range(n**k):
        s=[tb//(n**bt)%n for bt in range(k)];rt+=[s]
    return rt
def show(*inp,end='\n'):
    if show_flg:print(*inp,end=end)

YN=['YES','NO'];Yn=['Yes','No']
mo=10**9+7
inf=float('inf')
l_alp=string.ascii_lowercase

input=lambda: sys.stdin.readline().rstrip()

class Tree:
    def __init__(self,inp_size=None,init=True):
        self.LCA_init_stat=False
        self.ETtable=[]
        if init:
            self.stdin(inp_size)
        return

    def stdin(self,inp_size=None,index=1):
        if inp_size==None:
            self.size=int(input())
        else:
            self.size=inp_size
        self.edges,_=GI(self.size,self.size-1,index=index)
        return
    
    def listin(self,ls,index=0):
        self.size=len(ls)+1
        self.edges,_=GI(self.size,self.size-1,ls,index=index)
        return

    def __str__(self):
        return  str(self.edges)

    def dfs(self,x,func=lambda prv,nx,dist:prv+dist,root_v=0):
        q=deque()
        q.append(x)
        v=[-1]*self.size
        v[x]=root_v
        while q:
            c=q.pop()
            for nb,d in self.edges[c]:
                if v[nb]==-1:
                    q.append(nb)
                    v[nb]=func(v[c],nb,d)
        return v

    def EulerTour(self,x,func=lambda prv,nx,dist:prv+1,root_v=0):
        q=deque()
        q.append(x)
        depth=[None]*self.size
        depth[x]=root_v
        self.ETtable=[]
        self.ETdepth=[]
        self.ETin=[-1]*self.size
        self.ETout=[-1]*self.size
        cnt=0
        while q:
            c=q.pop()
            if c<0:
                ce=~c
            else:
                ce=c
                for nb,d in self.edges[ce]:
                    if depth[nb]==None:
                        q.append(~ce)
                        q.append(nb)
                        depth[nb]=depth[ce]+1
            self.ETtable.append(ce)
            self.ETdepth.append(depth[ce])
            if self.ETin[ce]==-1:
                self.ETin[ce]=cnt
            else:
                self.ETout[ce]=cnt
            cnt+=1
        return depth
    
    def LCA_init(self,root):
        self.EulerTour(root,func=lambda prv,nx,dist:prv+dist,root_v=0)
        self.st=SparseTable(self.ETdepth,init_func=min,init_idl=inf)
        self.LCA_init_stat=True
        return
    
    def LCA(self,root,x,y):
        if self.LCA_init_stat==False:
            self.LCA_init(root)
        xin,xout=self.ETin[x],self.ETout[x]
        yin,yout=self.ETin[y],self.ETout[y]
        a=min(xin,yin)
        b=max(xout,yout,xin,yin)
        id_of_min_dep_in_et=self.st.query_id(a,b+1)
        
        return self.ETtable[id_of_min_dep_in_et]

class SparseTable: 
    def __init__(self,ls,init_func=min,init_idl=float('inf')):
        self.func=init_func
        self.idl=init_idl
        self.size=len(ls)
        self.N0=self.size.bit_length()
        self.table=[ls[:]]
        self.index=[list(range(self.size))]
        self.lg=[0]*(self.size+1)
        
        for i in range(2,self.size+1):
            self.lg[i]=self.lg[i>>1]+1

        for i in range(self.N0):
            tmp=[self.func(self.table[i][j],self.table[i][min(j+(1<<i),self.size-1)]) for j in range(self.size)]
            tmp_id=[self.index[i][j] if self.table[i][j]==self.func(self.table[i][j],self.table[i][min(j+(1<<i),self.size-1)]) else self.index[i][min(j+(1<<i),self.size-1)] for j in range(self.size)]
            self.table+=[tmp]
            self.index+=[tmp_id]
    
    
    def query(self,l,r):
        
        N=self.lg[r-l]
        return self.func(self.table[N][l],self.table[N][r-(1<<N)])
    
    
    def query_id(self,l,r):
        
        N=self.lg[r-l]
        a,b=self.index[N][l],self.index[N][r-(1<<N)]
        if self.table[0][a]==self.func(self.table[N][l],self.table[N][r-(1<<N)]):
            b=a
        return b
    
    def __str__(self):
        return str(self.table[0])
        
    def print(self):
        for i in self.table:
            print(*i)

show_flg=False
show_flg=True
ans=0


n,q=LI()
ls=[]
col=dict()
e_len=dict()
for i in range(n-1):
    a,b,c,d=LI_()
    d+=1
    ls+=[(a,b,d)]
    
    eid=a*n+b if a<b else b*n+a
    col[eid]=c
    e_len[eid]=d
    
tr=Tree(init=False)
tr.listin(ls,index=0)

root=0
dist=tr.dfs(root,func=lambda prv_v,nx,dist:prv_v+dist)
dep=tr.EulerTour(root)
et=tr.ETtable

ad=[[0] for i in range(n)]
an=[[0] for i in range(n)]
index=[[] for i in range(n)]
for i in range(2*n-1-1):
    a,b=et[i],et[i+1]
    sign=1 if dep[a]<dep[b] else -1
    eid=a*n+b if a<b else b*n+a
    c=col[eid]
    dd=e_len[eid]*sign
    an[c]+=[an[c][-1]+sign]
    ad[c]+=[ad[c][-1]+dd]
    index[c]+=[i]

for i in range(q):
    x,y,u,v=LI_()
    y+=1
    lca=tr.LCA(root,u,v)
    path=dist[u]+dist[v]-dist[lca]*2
    
    ui=min(bisect.bisect_left(index[x],tr.ETin[u]),len(index[x]))
    vi=min(bisect.bisect_left(index[x],tr.ETin[v]),len(index[x]))
    ai=min(bisect.bisect_left(index[x],tr.ETin[lca]),len(index[x]))
    
    c_path=ad[x][ui]+ad[x][vi]-ad[x][ai]*2
    c_n=an[x][ui]+an[x][vi]-an[x][ai]*2
    ans=path-c_path+c_n*y
    print(ans)

Solution (Python):
import sys,bisect,string,math,time,functools,random
from heapq import heappush,heappop,heapify
from collections import deque,defaultdict,Counter
from itertools import permutations,combinations,groupby
def Golf():*a,=map(int,open(0))
def I():return int(input())
def S_():return input()
def IS():return input().split()
def LS():return [i for i in input().split()]
def LI():return [int(i) for i in input().split()]
def LI_():return [int(i)-1 for i in input().split()]
def NI(n):return [int(input()) for i in range(n)]
def NI_(n):return [int(input())-1 for i in range(n)]
def StoLI():return [ord(i)-97 for i in input()]
def ItoS(n):return chr(n+97)
def LtoS(ls):return ''.join([chr(i+97) for i in ls])
def GI(V,E,ls=None,Directed=False,index=1):
    org_inp=[];g=[[] for i in range(V)]
    FromStdin=True if ls==None else False
    for i in range(E):
        if FromStdin:
            inp=LI()
            org_inp.append(inp)
        else:
            inp=ls[i]
        if len(inp)==2:
            a,b=inp;c=1
        else:
            a,b,c=inp
        if index==1:a-=1;b-=1
        aa=(a,c);bb=(b,c);g[a].append(bb)
        if not Directed:g[b].append(aa)
    return g,org_inp
def GGI(h,w,search=None,replacement_of_found='.',mp_def={'

    mp=[boundary]*(w+2);found={}
    for i in range(h):
        s=input()
        for char in search:
            if char in s:
                found[char]=((i+1)*(w+2)+s.index(char)+1)
                mp_def[char]=mp_def[replacement_of_found]
        mp+=[boundary]+[mp_def[j] for j in s]+[boundary]
    mp+=[boundary]*(w+2)
    return h+2,w+2,mp,found
def TI(n):return GI(n,n-1)
def bit_combination(k,n=2):
    rt=[]
    for tb in range(n**k):
        s=[tb//(n**bt)%n for bt in range(k)];rt+=[s]
    return rt
def show(*inp,end='\n'):
    if show_flg:print(*inp,end=end)

YN=['YES','NO'];Yn=['Yes','No']
mo=10**9+7
inf=float('inf')
l_alp=string.ascii_lowercase

input=lambda: sys.stdin.readline().rstrip()

class Tree:
    def __init__(self,inp_size=None,init=True):
        self.LCA_init_stat=False
        self.ETtable=[]
        if init:
            self.stdin(inp_size)
        return

    def stdin(self,inp_size=None,index=1):
        if inp_size==None:
            self.size=int(input())
        else:
            self.size=inp_size
        self.edges,_=GI(self.size,self.size-1,index=index)
        return
    
    def listin(self,ls,index=0):
        self.size=len(ls)+1
        self.edges,_=GI(self.size,self.size-1,ls,index=index)
        return

    def __str__(self):
        return  str(self.edges)

    def dfs(self,x,func=lambda prv,nx,dist:prv+dist,root_v=0):
        q=deque()
        q.append(x)
        v=[-1]*self.size
        v[x]=root_v
        while q:
            c=q.pop()
            for nb,d in self.edges[c]:
                if v[nb]==-1:
                    q.append(nb)
                    v[nb]=func(v[c],nb,d)
        return v

    def EulerTour(self,x,func=lambda prv,nx,dist:prv+1,root_v=0):
        q=deque()
        q.append((-1,x))
        depth=[None]*self.size
        depth[x]=root_v
        et=[]
        while q:
            cb,ce=q.pop()
            et.append(ce)
            for nb,d in self.edges[ce]:
                if depth[nb]==None:
                    q.append((nb,ce))
                    q.append((ce,nb))
                    depth[nb]=func(depth[ce],nb,d)
        vid=[[-1,-1]for i in range(self.size)]
        for i,j in enumerate(et):
            if vid[j][0]==-1:
                vid[j][0]=i
            else:
                vid[j][1]=i
        self.ETtable=et[:]
        self.ETdepth=[depth[i] for i in et]
        self.ETid=vid[:]
        return depth,et,vid

    def FastEulerTour(self,x,func=lambda prv,nx,dist:prv+1,root_v=0):
        q=deque()
        q.append(x)
        depth=[None]*self.size
        depth[x]=root_v
        self.ETtable=[]
        self.ETdepth=[]
        self.ETin=[-1]*self.size
        self.ETout=[-1]*self.size
        cnt=0
        while q:
            c=q.pop()
            if c<0:
                ce=~c
            else:
                ce=c
                for nb,d in self.edges[ce]:
                    if depth[nb]==None:
                        q.append(~ce)
                        q.append(nb)
                        depth[nb]=depth[ce]+1
            self.ETtable.append(ce)
            self.ETdepth.append(depth[ce])
            if self.ETin[ce]==-1:
                self.ETin[ce]=cnt
            else:
                self.ETout[ce]=cnt
            cnt+=1
        return depth
    
    def LCA_init(self,root):
        self.FastEulerTour(root,func=lambda prv,nx,dist:prv+dist,root_v=0)
        self.st=SparseTable(self.ETdepth,init_func=min,init_idl=inf)
        self.LCA_init_stat=True
        return
    
    def LCA(self,root,x,y):
        if self.LCA_init_stat==False:
            self.LCA_init(root)
        xin,xout=self.ETin[x],self.ETout[x]
        yin,yout=self.ETin[y],self.ETout[y]
        a=min(xin,yin)
        b=max(xout,yout,xin,yin)
        id_of_min_dep_in_et=self.st.query_id(a,b+1)
        
        return self.ETtable[id_of_min_dep_in_et]

class SparseTable: 
    def __init__(self,ls,init_func=min,init_idl=float('inf')):
        self.func=init_func
        self.idl=init_idl
        self.size=len(ls)
        self.N0=self.size.bit_length()
        self.table=[ls[:]]
        self.index=[list(range(self.size))]
        self.lg=[0]*(self.size+1)
        
        for i in range(2,self.size+1):
            self.lg[i]=self.lg[i>>1]+1

        for i in range(self.N0):
            tmp=[self.func(self.table[i][j],self.table[i][min(j+(1<<i),self.size-1)]) for j in range(self.size)]
            tmp_id=[self.index[i][j] if self.table[i][j]==self.func(self.table[i][j],self.table[i][min(j+(1<<i),self.size-1)]) else self.index[i][min(j+(1<<i),self.size-1)] for j in range(self.size)]
            self.table+=[tmp]
            self.index+=[tmp_id]
    
    
    def query(self,l,r):
        
        N=self.lg[r-l]
        return self.func(self.table[N][l],self.table[N][r-(1<<N)])
    
    
    def query_id(self,l,r):
        
        N=self.lg[r-l]
        a,b=self.index[N][l],self.index[N][r-(1<<N)]
        if self.table[0][a]==self.func(self.table[N][l],self.table[N][r-(1<<N)]):
            b=a
        return b
    
    def __str__(self):
        return str(self.table[0])
        
    def print(self):
        for i in self.table:
            print(*i)

show_flg=False
show_flg=True
ans=0


n,q=LI()
ls=[]
col=dict()
e_len=dict()
for i in range(n-1):
    a,b,c,d=LI_()
    d+=1
    ls+=[(a,b,d)]
    if a>b:
        a,b=b,a
    col[a*n+b]=c
    e_len[a*n+b]=d

tr=Tree(init=False)
tr.listin(ls,index=0)

root=0
dist=tr.dfs(root,func=lambda prv_v,nx,dist:prv_v+dist)
dep=tr.FastEulerTour(root)
et=tr.ETtable


ad=[[0] for i in range(n)]
an=[[0] for i in range(n)]
index=[[] for i in range(n)]
for i in range(2*n-1-1):
    a,b=et[i],et[i+1]
    sign=1 if dep[a]<dep[b] else -1
    if a>b:
        a,b=b,a
    c=col[a*n+b]
    dd=e_len[a*n+b]*sign
    an[c]+=[an[c][-1]+sign]
    ad[c]+=[ad[c][-1]+dd]
    index[c]+=[i]

for i in range(q):
    x,y,u,v=LI_()
    y+=1
    lca=tr.LCA(root,u,v)
    dist_u=dist[u]-dist[lca]
    dist_v=dist[v]-dist[lca]
    path=dist_u+dist_v
    
    ui=bisect.bisect_left(index[x],tr.ETin[u])
    vi=bisect.bisect_left(index[x],tr.ETin[v])
    
    ai=bisect.bisect_left(index[x],tr.ETin[lca])
    ui=min(ui,len(index[x]))
    vi=min(vi,len(index[x]))
    ai=min(ai,len(index[x]))
    
    c_dist_u=ad[x][ui]-ad[x][ai]
    c_dist_v=ad[x][vi]-ad[x][ai]
    c_path=c_dist_u+c_dist_v
    c_n_u=an[x][ui]-an[x][ai]
    c_n_v=an[x][vi]-an[x][ai]
    c_n=c_n_u+c_n_v
    
    ans=path-c_path+c_n*y
    
    
    print(ans)

Solution (Python):
import sys,bisect,string,math,time,functools,random
from heapq import heappush,heappop,heapify
from collections import deque,defaultdict,Counter
from itertools import permutations,combinations,groupby
def Golf():*a,=map(int,open(0))
def I():return int(input())
def S_():return input()
def IS():return input().split()
def LS():return [i for i in input().split()]
def LI():return [int(i) for i in input().split()]
def LI_():return [int(i)-1 for i in input().split()]
def NI(n):return [int(input()) for i in range(n)]
def NI_(n):return [int(input())-1 for i in range(n)]
def StoLI():return [ord(i)-97 for i in input()]
def ItoS(n):return chr(n+97)
def LtoS(ls):return ''.join([chr(i+97) for i in ls])
def GI(V,E,ls=None,Directed=False,index=1):
    org_inp=[];g=[[] for i in range(V)]
    FromStdin=True if ls==None else False
    for i in range(E):
        if FromStdin:
            inp=LI()
            org_inp.append(inp)
        else:
            inp=ls[i]
        if len(inp)==2:
            a,b=inp;c=1
        else:
            a,b,c=inp
        if index==1:a-=1;b-=1
        aa=(a,c);bb=(b,c);g[a].append(bb)
        if not Directed:g[b].append(aa)
    return g,org_inp
def GGI(h,w,search=None,replacement_of_found='.',mp_def={'

    mp=[boundary]*(w+2);found={}
    for i in range(h):
        s=input()
        for char in search:
            if char in s:
                found[char]=((i+1)*(w+2)+s.index(char)+1)
                mp_def[char]=mp_def[replacement_of_found]
        mp+=[boundary]+[mp_def[j] for j in s]+[boundary]
    mp+=[boundary]*(w+2)
    return h+2,w+2,mp,found
def TI(n):return GI(n,n-1)
def bit_combination(k,n=2):
    rt=[]
    for tb in range(n**k):
        s=[tb//(n**bt)%n for bt in range(k)];rt+=[s]
    return rt
def show(*inp,end='\n'):
    if show_flg:print(*inp,end=end)

YN=['YES','NO'];Yn=['Yes','No']
mo=10**9+7
inf=float('inf')
l_alp=string.ascii_lowercase

input=lambda: sys.stdin.readline().rstrip()

class Tree:
    def __init__(self,inp_size=None,init=True):
        self.LCA_init_stat=False
        self.ETtable=[]
        if init:
            self.stdin(inp_size)
        return

    def stdin(self,inp_size=None,index=1):
        if inp_size==None:
            self.size=int(input())
        else:
            self.size=inp_size
        self.edges,_=GI(self.size,self.size-1,index=index)
        return
    
    def listin(self,ls,index=0):
        self.size=len(ls)+1
        self.edges,_=GI(self.size,self.size-1,ls,index=index)
        return

    def __str__(self):
        return  str(self.edges)

    def dfs(self,x,func=lambda prv,nx,dist:prv+dist,root_v=0):
        q=deque()
        q.append(x)
        v=[-1]*self.size
        v[x]=root_v
        while q:
            c=q.pop()
            for nb,d in self.edges[c]:
                if v[nb]==-1:
                    q.append(nb)
                    v[nb]=func(v[c],nb,d)
        return v

    def EulerTour(self,x,func=lambda prv,nx,dist:prv+1,root_v=0):
        q=deque()
        q.append((-1,x))
        depth=[None]*self.size
        depth[x]=root_v
        et=[]
        while q:
            cb,ce=q.pop()
            et.append(ce)
            for nb,d in self.edges[ce]:
                if depth[nb]==None:
                    q.append((nb,ce))
                    q.append((ce,nb))
                    depth[nb]=func(depth[ce],nb,d)
        vid=[[-1,-1]for i in range(self.size)]
        for i,j in enumerate(et):
            if vid[j][0]==-1:
                vid[j][0]=i
            else:
                vid[j][1]=i
        self.ETtable=et[:]
        self.ETdepth=[depth[i] for i in et]
        self.ETid=vid[:]
        return depth,et,vid

    def FastEulerTour(self,x,func=lambda prv,nx,dist:prv+1,root_v=0):
        q=deque()
        q.append(x)
        depth=[None]*self.size
        depth[x]=root_v
        self.ETtable=[]
        self.ETin=[-1]*self.size
        self.ETout=[-1]*self.size
        cnt=0
        while q:
            c=q.pop()
            if c<0:
                ce=~c
            else:
                ce=c
                
                
                for nb,d in self.edges[ce]:
                    if depth[nb]==None:
                        q.append(~ce)
                        q.append(nb)
                        
                        
                        depth[nb]=depth[ce]+1
            self.ETtable.append(ce)
            if self.ETin[ce]==-1:
                self.ETin[ce]=cnt
            else:
                self.ETout[ce]=cnt
            cnt+=1
        
        self.ETdepth=[depth[i] for i in self.ETtable]
        return depth
    
    def LCA_init(self,root):
        self.FastEulerTour(root,func=lambda prv,nx,dist:prv+dist,root_v=0)
        self.st=SparseTable(self.ETdepth,init_func=min,init_idl=inf)
        self.LCA_init_stat=True
        return
    
    def LCA(self,root,x,y):
        if self.LCA_init_stat==False:
            self.LCA_init(root)
        xin,xout=self.ETin[x],self.ETout[x]
        yin,yout=self.ETin[y],self.ETout[y]
        a=min(xin,yin)
        b=max(xout,yout,xin,yin)
        id_of_min_dep_in_et=self.st.query_id(a,b+1)
        
        return self.ETtable[id_of_min_dep_in_et]

class SparseTable: 
    def __init__(self,ls,init_func=min,init_idl=float('inf')):
        self.func=init_func
        self.idl=init_idl
        self.size=len(ls)
        self.N0=self.size.bit_length()
        self.table=[ls[:]]
        self.index=[list(range(self.size))]
        self.lg=[0]*(self.size+1)
        
        for i in range(2,self.size+1):
            self.lg[i]=self.lg[i>>1]+1

        for i in range(self.N0):
            tmp=[self.func(self.table[i][j],self.table[i][min(j+(1<<i),self.size-1)]) for j in range(self.size)]
            tmp_id=[self.index[i][j] if self.table[i][j]==self.func(self.table[i][j],self.table[i][min(j+(1<<i),self.size-1)]) else self.index[i][min(j+(1<<i),self.size-1)] for j in range(self.size)]
            self.table+=[tmp]
            self.index+=[tmp_id]
    
    
    def query(self,l,r):
        
        N=self.lg[r-l]
        return self.func(self.table[N][l],self.table[N][r-(1<<N)])
    
    
    def query_id(self,l,r):
        
        N=self.lg[r-l]
        a,b=self.index[N][l],self.index[N][r-(1<<N)]
        if self.table[0][a]==self.func(self.table[N][l],self.table[N][r-(1<<N)]):
            b=a
        return b
    
    def __str__(self):
        return str(self.table[0])
        
    def print(self):
        for i in self.table:
            print(*i)

show_flg=False
show_flg=True
ans=0


n,q=LI()
ls=[]
col=dict()
e_len=dict()
for i in range(n-1):
    a,b,c,d=LI_()
    d+=1
    ls+=[(a,b,d)]
    if a>b:
        a,b=b,a
    col[a*n+b]=c
    e_len[a*n+b]=d

tr=Tree(init=False)
tr.listin(ls,index=0)

root=0
dist=tr.dfs(root,func=lambda prv_v,nx,dist:prv_v+dist)
dep=tr.FastEulerTour(root)
et=tr.ETtable


ad=[[0] for i in range(n)]
an=[[0] for i in range(n)]
index=[[] for i in range(n)]
for i in range(2*n-1-1):
    a,b=et[i],et[i+1]
    sign=1 if dep[a]<dep[b] else -1
    if a>b:
        a,b=b,a
    c=col[a*n+b]
    dd=e_len[a*n+b]*sign
    an[c]+=[an[c][-1]+sign]
    ad[c]+=[ad[c][-1]+dd]
    index[c]+=[i]
    

for i in range(q):
    x,y,u,v=LI_()
    y+=1
    lca=tr.LCA(root,u,v)
    dist_u=dist[u]-dist[lca]
    dist_v=dist[v]-dist[lca]
    path=dist_u+dist_v
    
    ui=bisect.bisect_left(index[x],tr.ETin[u])
    vi=bisect.bisect_left(index[x],tr.ETin[v])
    
    ai=bisect.bisect_left(index[x],tr.ETin[lca])
    ui=min(ui,len(index[x]))
    vi=min(vi,len(index[x]))
    ai=min(ai,len(index[x]))
    
    
    c_dist_u=ad[x][ui]-ad[x][ai]
    c_dist_v=ad[x][vi]-ad[x][ai]
    c_path=c_dist_u+c_dist_v
    c_n_u=an[x][ui]-an[x][ai]
    c_n_v=an[x][vi]-an[x][ai]
    c_n=c_n_u+c_n_v
    
    ans=path-c_path+c_n*y
    
    
    print(ans)

Solution (Python):

import sys
from collections import defaultdict
readline = sys.stdin.readline
N, Q = map(int, readline().split())

def dfs_w(v, d):
    vs = set([1])
    S, F, depth, depthh = [], [None]+[0]*N, [-1] + [0]*N, [0] + [0]*N
    iin = [[(0, 0, 0)] for _ in range(N)]

    stack, path = [(1, 0, 0)], [0]
    while stack:
        v, cc, dpd = stack.pop()
        if v > 0:
            parent = path[-1]
            path.append(v)

            F[v] = len(S)
            depth[v], depthh[v] = depth[parent] + 1, depthh[parent] + dpd
            iin[cc].append((iin[cc][-1][0]+1, iin[cc][-1][1]+dpd, len(S)))

            S.append(v)
            for u, ucc, udpd in d[v]:
                if u in vs:
                    continue
                vs.add(u)
                stack += [(-v, ucc, udpd), (u, ucc, udpd)]
        else:
            path.pop()
            iin[cc].append((iin[cc][-1][0]-1, iin[cc][-1][1]-dpd, len(S)))
            S.append(-v)

    return S, F, depth, depthh, iin

class SegTree:
    def __init__(self, init_val, n, ide_ele, seg_func):
        self.segfunc = seg_func
        self.num = 2**(n-1).bit_length()
        self.ide_ele = ide_ele
        self.seg=[self.ide_ele]*2*self.num
        for i in range(n):
            self.seg[i+self.num-1]=init_val[i]    
        for i in range(self.num-2,-1,-1) :
            self.seg[i]=self.segfunc(self.seg[2*i+1],self.seg[2*i+2]) 
        
    def update(self, k, x):
        k += self.num-1
        self.seg[k] = x
        while k+1:
            k = (k-1)//2
            self.seg[k] = self.segfunc(self.seg[k*2+1],self.seg[k*2+2])
        
    def query(self, p, q):
        if q<=p:
            return self.ide_ele
        p += self.num-1
        q += self.num-2
        res=self.ide_ele
        while q-p>1:
            if p&1 == 0:
                res = self.segfunc(res,self.seg[p])
            if q&1 == 1:
                res = self.segfunc(res,self.seg[q])
                q -= 1
            p = p//2
            q = (q-1)//2
        if p == q:
            res = self.segfunc(res,self.seg[p])
        else:
            res = self.segfunc(self.segfunc(res,self.seg[p]),self.seg[q])
        return res

def bsearch(target, min_i, max_i, func):
    
    if func(max_i) <= target:
        return max_i
    if target < func(min_i):
        return None
    index = (max_i + min_i)//2
    while True:
        if func(index) <= target:
            if target < func(index+1):
                return index
            index, min_i = (index+1 + max_i)//2, index+1
            continue
        index, max_i = (index-1 + min_i)//2, index-1

def process():
    G = [set() for _ in range(N+1)]
    for _ in range(N-1):
        a, b, c, d = map(int, readline().split())
        G[a].add((b,c,d))
        G[b].add((a,c,d))

    S, F, depth, depthh, iin = dfs_w(1, G)

    stree = SegTree([(depth[v], i) for i, v in enumerate(S)], len(S), (N, None), min)
    for _ in range(Q):
        x, y, u, v = map(int, readline().split())
        fu, fv = sorted([F[u], F[v]])
        cc = S[stree.query(fu, fv+1)[1]]

        (fuy, fuv, _), (fvy, fvv, _), (fccy, fccv, _) = [iin[x][bsearch(index, 0, len(iin[x])-1, lambda j: iin[x][j][2])] for index in [fu, fv, F[cc]]]
        r = depthh[u] + depthh[v] - 2*depthh[cc] + (fuy + fvy - 2 * fccy) * y - (fuv + fvv - 2 * fccv)
        print(r)

if __name__ == '__main__':
    process()

Solution (Python):

import sys
from collections import defaultdict
readline = sys.stdin.readline
N, Q = map(int, readline().split())

def dfs_w(v, d):
    vs = set([1])
    S, F, depth, depthh = [], [None]+[0]*N, [-1] + [0]*N, [0] + [0]*N
    iin = [[(0, 0, 0)] for _ in range(N)]

    stack, path = [(1, 0, 0)], [0]
    while stack:
        v, cc, dpd = stack.pop()
        if v > 0:
            parent = path[-1]
            path.append(v)

            F[v] = len(S)
            depth[v], depthh[v] = depth[parent] + 1, depthh[parent] + dpd
            iin[cc].append((iin[cc][-1][0]+1, iin[cc][-1][1]+dpd, len(S)))

            S.append(v)
            for u, ucc, udpd in d[v]:
                if u in vs:
                    continue
                vs.add(u)
                stack += [(-v, ucc, udpd), (u, ucc, udpd)]
        else:
            path.pop()
            iin[cc].append((iin[cc][-1][0]-1, iin[cc][-1][1]-dpd, len(S)))
            S.append(v)

    return S, F, depth, depthh, iin

class SegTree:
    def __init__(self, init_val, n, ide_ele, seg_func):
        self.segfunc = seg_func
        self.num = 2**(n-1).bit_length()
        self.ide_ele = ide_ele
        self.seg=[self.ide_ele]*2*self.num
        for i in range(n):
            self.seg[i+self.num-1]=init_val[i]    
        for i in range(self.num-2,-1,-1) :
            self.seg[i]=self.segfunc(self.seg[2*i+1],self.seg[2*i+2]) 
        
    def update(self, k, x):
        k += self.num-1
        self.seg[k] = x
        while k+1:
            k = (k-1)//2
            self.seg[k] = self.segfunc(self.seg[k*2+1],self.seg[k*2+2])
        
    def query(self, p, q):
        if q<=p:
            return self.ide_ele
        p += self.num-1
        q += self.num-2
        res=self.ide_ele
        while q-p>1:
            if p&1 == 0:
                res = self.segfunc(res,self.seg[p])
            if q&1 == 1:
                res = self.segfunc(res,self.seg[q])
                q -= 1
            p = p//2
            q = (q-1)//2
        if p == q:
            res = self.segfunc(res,self.seg[p])
        else:
            res = self.segfunc(self.segfunc(res,self.seg[p]),self.seg[q])
        return res

def bsearch(target, min_i, max_i, func):
    
    if func(max_i) <= target:
        return max_i
    if target < func(min_i):
        return None
    index = (max_i + min_i)//2
    while True:
        if func(index) <= target:
            if target < func(index+1):
                return index
            index, min_i = (index+1 + max_i)//2, index+1
            continue
        index, max_i = (index-1 + min_i)//2, index-1

def process():
    G = [set() for _ in range(N+1)]
    for _ in range(N-1):
        a, b, c, d = map(int, readline().split())
        G[a].add((b,c,d))
        G[b].add((a,c,d))

    S, F, depth, depthh, iin = dfs_w(1, G)

    stree = SegTree([(depth[abs(v)], i) for i, v in enumerate(S)], len(S), (N, None), min)
    for _ in range(Q):
        x, y, u, v = map(int, readline().split())
        fu, fv = sorted([F[u], F[v]])
        cc = abs(S[stree.query(fu, fv+1)[1]])

        (fuy, fuv, _), (fvy, fvv, _), (fccy, fccv, _) = [iin[x][bsearch(index, 0, len(iin[x])-1, lambda j: iin[x][j][2])] for index in [fu, fv, F[cc]]]
        r = depthh[u] + depthh[v] - 2*depthh[cc] + (fuy + fvy - 2 * fccy) * y - (fuv + fvv - 2 * fccv)
        print(r)

if __name__ == '__main__':
    process()