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.



Sample input:
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:
130
200
60

Submission status: Accepted

Solution code:
import sys,bisect,string,math,time,functools,random,fractions
from heapq import heappush,heappop,heapify
from collections import deque,defaultdict,Counter
from itertools import permutations,combinations,groupby
rep=range
def Golf():n,*t=map(int,open(0).read().split())
def I():return int(input())
def S_():return input()
def IS():return input().split()
def LS():return [i for i in input().split()]
def MI():return map(int,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 RA():return map(int,open(0).read().split())
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={'#':1,'.':0},boundary=1):
    #h,w,g,sg=GGI(h,w,search=['S','G'],replacement_of_found='.',mp_def={'#':1,'.':0},boundary=1) # sample usage
    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 accum(ls):
    rt=[0]
    for i in ls:rt+=[rt[-1]+i]
    return rt
def bit_combination(n,base=2):
    rt=[]
    for tb in range(base**n):s=[tb//(base**bt)%base for bt in range(n)];rt+=[s]
    return rt
def gcd(x,y):
    if y==0:return x
    if x%y==0:return y
    while x%y!=0:x,y=y,x%y
    return y
def YN(x):print(['NO','YES'][x])
def Yn(x):print(['No','Yes'][x])
def show(*inp,end='\n'):
    if show_flg:print(*inp,end=end)

mo=10**9+7
inf=float('inf')
FourNb=[(-1,0),(1,0),(0,1),(0,-1)];EightNb=[(-1,0),(1,0),(0,1),(0,-1),(1,1),(-1,-1),(1,-1),(-1,1)];compas=dict(zip('WENS',FourNb));cursol=dict(zip('LRUD',FourNb))
l_alp=string.ascii_lowercase
#sys.setrecursionlimit(10**7)
read=sys.stdin.buffer.read
readline=sys.stdin.buffer.readline
input=lambda: sys.stdin.readline().rstrip()

class Tree:
    def __init__(self,inp_size=None,ls=None,init=True,index=1):
        self.LCA_init_stat=False
        self.ETtable=[]
        if init:
            if ls==None:
                self.stdin(inp_size,index=index)
            else:
                self.node_size=len(ls)+1
                self.edges,_=GI(self.node_size,self.node_size-1,ls,index=index)
        return
 
    def stdin(self,inp_size=None,index=1):
        if inp_size==None:
            self.node_size=int(input())
        else:
            self.node_size=inp_size
        self.edges,_=GI(self.node_size,self.node_size-1,index=index)
        return
    
    def listin(self,ls,index=0):
        self.node_size=len(ls)+1
        self.edges,_=GI(self.node_size,self.node_size-1,ls,index=index)
        return
 
    def dfs(self,x,func=lambda pr,prv,nx,dist:prv+dist,root_v=0):
        q=deque([x])
        v=[None]*self.node_size
        v[x]=root_v
        while q:
            c=q.pop()
            for nb,d in self.edges[c]:
                if v[nb]==None:
                    q.append(nb)
                    v[nb]=func(c,v[c],nb,d)
        return v
 
    def bfs(self,x,func=lambda pr,prv,nx,dist:prv+dist,root_v=0):
        q=deque([x])
        v=[None]*self.node_size
        v[x]=root_v
        while q:
            c=q.popleft()
            for nb,d in self.edges[c]:
                if v[nb]==None:
                    q.append(nb)
                    v[nb]=func(c,v[c],nb,d)
        return v
 
    def parent(self,x):
        return self.dfs(0,func=lambda pr,prv,nx,dist:pr,root_v=-1)
 
    def topological_sort(self,x):  # return topological sort of the tree
        tps=[]
        q=deque([x])
        v=[None]*self.node_size
        v[x]=0
        while q:
            c=q.popleft()
            tps.append(c)
            for nb,d in self.edges[c]:
                if v[nb]==None:
                    q.append(nb)
                    v[nb]=0
        return tps
 
    def EulerTour(self,x):
        q=deque()
        q.append(x)
        self.depth=[None]*self.node_size
        self.depth[x]=0
        self.ETtable=[]
        self.ETdepth=[]
        self.ETin=[-1]*self.node_size
        self.ETout=[-1]*self.node_size
        cnt=0
        while q:
            c=q.pop()
            if c<0:
                ce=~c
            else:
                ce=c
                for nb,d in self.edges[ce]:
                    if self.depth[nb]==None:
                        q.append(~ce)
                        q.append(nb)
                        self.depth[nb]=self.depth[ce]+1
            self.ETtable.append(ce)
            self.ETdepth.append(self.depth[ce])
            if self.ETin[ce]==-1:
                self.ETin[ce]=cnt
            else:
                self.ETout[ce]=cnt
            cnt+=1
        return
    
    def doubling_LCA(self,root,x,y):
        if self.LCA_init_stat==False:
            self.depth=[None]*self.node_size
            self.depth=self.bfs(0,func=lambda pr,prv,nxt,dist:prv+1)
            self.par=self.bfs(0,func=lambda pr,prv,nxt,dist:pr)
            self.db=[self.par]
            for i in range(self.node_size.bit_length()):
                #show(self.db)
                self.db+=[[self.db[-1][self.db[-1][i]] for i in range(self.node_size)]]
            self.LCA_init_stat=True
        dx=self.depth[x]
        dy=self.depth[y]
        if dx>dy:
            dx,dy=dy,dx
        c=self.node_size.bit_length()
        while c>0:
            if dx+c<=dy:
                x=self.db[c][x]
                dx+=1<<c
            c>>=1
        
        if x==y:
            return x
        
        c=self.node_size.bit_length()
        while c>0:
            if self.db[c][x]!=self.db[c][y]:
                x=self.db[c][x]
                y=self.db[c][y]
            c>>=1
        
        return self.par[x]
        
    def LCA_init(self,root):
        self.EulerTour(root)
        self.st=SparseTable(self.ETdepth,init_func=min,init_idl=inf)
        #self.st=SegTree(self.node_size*2-1,self.ETdepth,function=min,ide=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]
 
    def __str__(self):
        return  str(self.edges)
 
    def show(self):
        if all([all([d==1 for nd,d in e]) for e in self.edges]):
            print( [[nd for nd,d in e] for e in self.edges] )
        else:
            print(self)
 
    def dfs2(self,x,func=lambda pr,prv,nx,dist:prv+dist,root_v=0):
        q=deque([x])
        v=[None]*self.node_size
        v[x]=root_v
        dfs_tr=[x]
        while q:
            c=q.pop()
            for nb,d in self.edges[c]:
                if v[nb]==None:
                    q.append(nb)
                    v[nb]=func(c,v[c],nb,d)
                    dfs_tr+=nb,
        return v,dfs_tr

class SparseTable: # O(N log N) for init, O(1) for query(l,r)
    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]
    
    # return func of [l,r)
    def query(self,l,r):
        if r>self.size:r=self.size
        #N=(r-l).bit_length()-1
        N=self.lg[r-l]
        return self.func(self.table[N][l],self.table[N][max(0,r-(1<<N))])
    
    # return index of which val[i] = func of v among [l,r)
    def query_id(self,l,r):
        if r>self.size:r=self.size
        #N=(r-l).bit_length()-1
        N=self.lg[r-l]
        a,b=self.index[N][l],self.index[N][max(0,r-(1<<N))]
        if self.table[0][a]==self.func(self.table[N][l],self.table[N][max(0,r-(1<<N))]):
            b=a
        return b
    
    # return boundary index of r such that func({table[i]} =< x , i in [pos,r]
    def right_bound(self,pos,x):
        k=(self.size-pos).bit_length()
        for j in range(k)[::-1]:
            nx=pos+(1<<j)
            if nx<n and self.query(pos,nx+1)<=x:
                pos+=(1<<j)
        return pos
    
    # return boundary index of l such that func({table[i]} =< x , i in [l,pos]
    def left_bound(self,pos,x):
        k=pos.bit_length()
        for j in range(k)[::-1]:
            nx=pos-(1<<j)
            if 0<=nx and self.query(nx,pos+1)<=x:
                pos-=(1<<j)
        return pos

    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=deque()
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)
tr.EulerTour(0)
dep=tr.depth
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(n):
    ad[i]+=[ad[i][-1]]
    an[i]+=[an[i][-1]]
 
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=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])
    
    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)

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(10**6+1) #再帰関数の上限,10**5以上の場合python


def input(): 
    x=sys.stdin.readline()
    return x[:-1] if x[-1]=="\n" else x
def printe(*x):print("## ",*x,file=sys.stderr)
def printl(li): _=print(*li, sep="\n") if li else None


#N, Q = map(int, input().split())
N, Q = map(int, input().split())
#A = tuple(map(int, input().split())) #1行ベクトル
#L = tuple(int(input()) for i in range(N)) #改行ベクトル
#S = tuple(tuple(map(int, input().split())) for i in range(N)) #改行行列

edge = [[] for i in range(N)]
for i in range(N-1):#木の場合M=N-1
    a,b,c,w = map(int,input().split())
    edge[a-1].append((b-1,c-1,w))
    edge[b-1].append((a-1,c-1,w)) #有向のばあいコメントアウト



#ダブリングによるLCA, 前処理NlogN, 呼び出しlogN, 安定  
def dfs(start):
    q=[(start,-1,0,0)]
    pars=[-1]*N
    depth=[-1]*N
    dist=[-1]*N
    while len(q):
        e,p,d,dis=q.pop()#ここをpopleftにすると幅優先探索BFSになる
        if depth[e]!=-1:continue
        pars[e]=p
        depth[e]=d
        dist[e]=dis
        for ne,c,w in edge[e]:
            q.append((ne,e,d+1,dis+w))
    return pars,depth,dist
pars,d,dist=dfs(0)
ln=N.bit_length()
dp=[[-1]*N for _ in range(ln+1)]
dp[0]=pars
for i in range(1,ln+1):
    for j in range(N):
        dp[i][j]=dp[i-1][dp[i-1][j]]


# LCAの計算
def lca(u, v):
    du = d[u]; dv = d[v]
    if du > dv:
        du, dv = dv, du
        u,v=v,u
    dif=dv-du
    for i in range(ln+1):
        if (dif>>i)&1:
            v=dp[i][v]
    if u==v:return u
    for i in range(ln,-1,-1):
        pu=dp[i][u];pv=dp[i][v]
        if pu!=pv:
            u,v=pu,pv
    return pars[u]

q=Q
qs = tuple(tuple(map(int, input().split())) for i in range(Q)) #改行行列
ans=[0]*Q
qn=[[] for _ in range(N)]
for i,(x,y,u,v) in enumerate(qs):
    ans[i]=dist[u-1]+dist[v-1]-2*dist[lca(u-1,v-1)]
    qn[u-1].append((i,x-1,y,1))
    qn[v-1].append((i,x-1,y,1))
    qn[lca(u-1,v-1)].append((i,x-1,y,-2))

cc=[[0,0] for _ in range(N-1)]

dfq=[(0,None,0,-1)]
def dfs2(e,c,d,p):
    if c!=None:
        cc[c][0]+=1
        cc[c][1]+=d
    for qi,x,y,sgn in qn[e]:
        ans[qi]+=(y*cc[x][0]-cc[x][1])*sgn
    for ne,nc,nd in edge[e]:
        if ne==pars[e]:continue
        dfs2(ne,nc,nd,e)
    if c!=None:
        cc[c][0]-=1
        cc[c][1]-=d
dfs2(0,-1,0,None)
printl(ans)

# n=N
# A = [0]*q
# C = [[] for _ in range(n)]
# num = [0]*n
# cum = [0]*n
# for i in range(q):
#   x, y, u, v = map(int, input().split())
#   u -= 1
#   v -= 1
#   a = lca(u, v)
#   C[u].append((i, x, y, 1))
#   C[v].append((i, x, y, 1))
#   C[a].append((i, x, y, -2))
# dist = 0
# stack = [0]
# def dfs2(v):
#   global dist
#   for i, x, y, b in C[v]:
#     A[i] += (dist + num[x]*y - cum[x]) * b
#   for nv, c, d in edge[v]:
#     c+=1
#     if nv ==pars[v]:continue
#     dist += d
#     num[c] += 1
#     cum[c] += d
#     dfs2(nv)
#     dist -= d
#     num[c] -= 1
#     cum[c] -= d
# dfs2(0)
# print(*A, sep="\n")

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(10**6+1) #再帰関数の上限,10**5以上の場合python


def input(): 
    x=sys.stdin.readline()
    return x[:-1] if x[-1]=="\n" else x
def printe(*x):print("## ",*x,file=sys.stderr)
def printl(li): _=print(*li, sep="\n") if li else None


#N, Q = map(int, input().split())
N, Q = map(int, input().split())
#A = tuple(map(int, input().split())) #1行ベクトル
#L = tuple(int(input()) for i in range(N)) #改行ベクトル
#S = tuple(tuple(map(int, input().split())) for i in range(N)) #改行行列

edge = [[] for i in range(N)]
for i in range(N-1):#木の場合M=N-1
    a,b,c,w = map(int,input().split())
    edge[a-1].append((b-1,c-1,w))
    edge[b-1].append((a-1,c-1,w)) #有向のばあいコメントアウト



#ダブリングによるLCA, 前処理NlogN, 呼び出しlogN, 安定  
def dfs(start):
    q=[(start,-1,0,0)]
    pars=[-1]*N
    depth=[-1]*N
    dist=[-1]*N
    while len(q):
        e,p,d,dis=q.pop()#ここをpopleftにすると幅優先探索BFSになる
        if depth[e]!=-1:continue
        pars[e]=p
        depth[e]=d
        dist[e]=dis
        for ne,c,w in edge[e]:
            q.append((ne,e,d+1,dis+w))
    return pars,depth,dist
pars,d,dist=dfs(0)
ln=N.bit_length()
dp=[[-1]*N for _ in range(ln+1)]
dp[0]=pars
for i in range(1,ln+1):
    for j in range(N):
        dp[i][j]=dp[i-1][dp[i-1][j]]


# LCAの計算
def lca(u, v):
    du = d[u]; dv = d[v]
    if du > dv:
        du, dv = dv, du
        u,v=v,u
    dif=dv-du
    for i in range(ln+1):
        if (dif>>i)&1:
            v=dp[i][v]
    if u==v:return u
    for i in range(ln,-1,-1):
        pu=dp[i][u];pv=dp[i][v]
        if pu!=pv:
            u,v=pu,pv
    return pars[u]

q=Q
qs = tuple(tuple(map(int, input().split())) for i in range(Q)) #改行行列
ans=[0]*Q
qn=[[] for _ in range(N)]
for i,(x,y,u,v) in enumerate(qs):
    ans[i]=dist[u-1]+dist[v-1]-2*dist[lca(u-1,v-1)]
    qn[u-1].append((i,x-1,y,1))
    qn[v-1].append((i,x-1,y,1))
    qn[lca(u-1,v-1)].append((i,x-1,y,-2))
cnt=[0]*Q
#printe(qn)

qc=[[0,0] for _ in range(Q)]
cc=[[0,0] for _ in range(N-1)]

dfq=[(0,None,0,-1)]
def dfs2(e):
    for qi,x,y,sgn in qn[e]:
        ans[qi]+=(y*cc[x][0]-cc[x][1])*sgn
    for ne,c,nd in edge[e]:
        if ne==pars[e]:continue
        if c!=None:
            cc[c][0]+=1
            cc[c][1]+=nd
        dfs2(ne)
        if c!=None:
            cc[c][0]-=1
            cc[c][1]-=nd
dfs2(0)
printl(ans)

# n=N
# A = [0]*q
# C = [[] for _ in range(n)]
# num = [0]*n
# cum = [0]*n
# for i in range(q):
#   x, y, u, v = map(int, input().split())
#   u -= 1
#   v -= 1
#   a = lca(u, v)
#   C[u].append((i, x, y, 1))
#   C[v].append((i, x, y, 1))
#   C[a].append((i, x, y, -2))
# dist = 0
# stack = [0]
# def dfs2(v):
#   global dist
#   for i, x, y, b in C[v]:
#     A[i] += (dist + num[x]*y - cum[x]) * b
#   for nv, c, d in edge[v]:
#     c+=1
#     if nv ==pars[v]:continue
#     dist += d
#     num[c] += 1
#     cum[c] += d
#     dfs2(nv)
#     dist -= d
#     num[c] -= 1
#     cum[c] -= d
# dfs2(0)
# print(*A, sep="\n")

Submission status: Accepted

Solution code:
import sys
sys.setrecursionlimit(10**6+1) #再帰関数の上限,10**5以上の場合python


def input(): 
    x=sys.stdin.readline()
    return x[:-1] if x[-1]=="\n" else x
def printe(*x):print("## ",*x,file=sys.stderr)
def printl(li): _=print(*li, sep="\n") if li else None


#N, Q = map(int, input().split())
N, Q = map(int, input().split())
#A = tuple(map(int, input().split())) #1行ベクトル
#L = tuple(int(input()) for i in range(N)) #改行ベクトル
#S = tuple(tuple(map(int, input().split())) for i in range(N)) #改行行列

edge = [[] for i in range(N)]
for i in range(N-1):#木の場合M=N-1
    a,b,c,w = map(int,input().split())
    edge[a-1].append((b-1,c-1,w))
    edge[b-1].append((a-1,c-1,w)) #有向のばあいコメントアウト



#ダブリングによるLCA, 前処理NlogN, 呼び出しlogN, 安定  
def dfs(start):
    q=[(start,-1,0,0)]
    pars=[-1]*N
    depth=[-1]*N
    dist=[-1]*N
    while len(q):
        e,p,d,dis=q.pop()#ここをpopleftにすると幅優先探索BFSになる
        if depth[e]!=-1:continue
        pars[e]=p
        depth[e]=d
        dist[e]=dis
        for ne,c,w in edge[e]:
            q.append((ne,e,d+1,dis+w))
    return pars,depth,dist
pars,d,dist=dfs(0)
ln=N.bit_length()
dp=[[-1]*N for _ in range(ln+1)]
dp[0]=pars
for i in range(1,ln+1):
    for j in range(N):
        dp[i][j]=dp[i-1][dp[i-1][j]]


# LCAの計算
def lca(u, v):
    du = d[u]; dv = d[v]
    if du > dv:
        du, dv = dv, du
        u,v=v,u
    dif=dv-du
    for i in range(ln+1):
        if (dif>>i)&1:
            v=dp[i][v]
    if u==v:return u
    for i in range(ln,-1,-1):
        pu=dp[i][u];pv=dp[i][v]
        if pu!=pv:
            u,v=pu,pv
    return pars[u]

q=Q
#qs = tuple(tuple(map(int, input().split())) for i in range(Q)) #改行行列
# ans=[0]*Q
# qn=[[] for _ in range(N)]
# for i,(x,y,u,v) in enumerate(qs):
#     ans[i]=dist[u-1]+dist[v-1]-dist[lca(u-1,v-1)]
#     qn[u-1].append((i,x-1,y))
#     qn[v-1].append((i,x-1,y))
# cnt=[0]*Q
# #printe(qn)

# qc=[[0,0] for _ in range(Q)]
# cc=[[0,0] for _ in range(N-1)]

# dfq=[(0,None,0,-1)]
# def dfs2(e,c,d,p):
#     if c!=None:
#         cc[c][0]+=1
#         cc[c][1]+=d
#     for qi,x,y in qn[e]:
#         if cnt[qi]==0:
#             qc[qi][0]-=cc[x][0]
#             qc[qi][1]-=cc[x][1]
#         elif cnt[qi]==1:
#             qc[qi][0]+=cc[x][0]
#             qc[qi][1]+=cc[x][1]
#             ans[qi]+=y*qc[qi][0]-qc[qi][1]
#         cnt[qi]+=1
#     for ne,nc,nd in edge[e]:
#         if ne==par[e]:continue
#         dfs2(ne,nc,nd,e)
#     if c!=None:
#         cc[c][0]+=1
#         cc[c][1]+=d
# dfs2(0)
# printl(ans)
n=N
A = [0]*q
C = [[] for _ in range(n)]
num = [0]*n
cum = [0]*n
for i in range(q):
  x, y, u, v = map(int, input().split())
  u -= 1
  v -= 1
  a = lca(u, v)
  C[u].append((i, x, y, 1))
  C[v].append((i, x, y, 1))
  C[a].append((i, x, y, -2))
dist = 0
stack = [0]
def dfs2(v):
  global dist
  for i, x, y, b in C[v]:
    A[i] += (dist + num[x]*y - cum[x]) * b
  for nv, c, d in edge[v]:
    c+=1
    if nv ==pars[v]:continue
    dist += d
    num[c] += 1
    cum[c] += d
    dfs2(nv)
    dist -= d
    num[c] -= 1
    cum[c] -= d
dfs2(0)
print(*A, sep="\n")

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**7)

class LCA:
    def __init__(self, edge, root):
        self.l = len(edge)
        self.stack = []
        self.stack.append((root, 0))
        self.vs = []
        self.depth = [0]*self.l
        self.firstVisited = [-1]*self.l
        while self.stack:
            v, d = self.stack[-1]
            if self.firstVisited[v] == -1:
                self.firstVisited[v] = len(self.vs)
            self.vs.append(v)
            self.depth[v] = d
            if edge[v]:
                self.stack.append((edge[v].pop(), d+1))
            else:
                self.stack.pop()
        
        self.n = len(self.vs)
        self.INF = (self.l, self.l)
        self.N0 = 1 << (self.n-1).bit_length()
        self.seg = [self.INF]*(self.N0 << 1)
        for i, v in enumerate(self.vs, self.N0):
            self.seg[i] = (self.depth[v], v)
        for i in range(self.N0-1, 0, -1):
            self.seg[i] = min(self.seg[2*i], self.seg[2*i+1])
    
    def _query(self, l, r):
        res = self.INF
        l += self.N0
        r += self.N0
        while l < r:
            if r & 1:
                res = min(res, self.seg[r-1])
            if l & 1:
                res = min(res, self.seg[l])
                l += 1
            l >>= 1
            r >>= 1
     
        return res

    def query(self, u, v):
        fu, fv = self.firstVisited[u], self.firstVisited[v]
        if fu > fv:
            fu, fv = fv, fu
        return self._query(fu, fv+1)[1]

n, q = map(int, input().split())
T = [[] for _ in range(n)]
for _ in range(n-1):
  a, b, c, d = map(int, input().split())
  a -= 1
  b -= 1
  T[a].append((b, c, d))
  T[b].append((a, c, d))
G = [[] for _ in range(n)]
edge = [[] for _ in range(n)]
stack = [(0, -1)]
while stack:
  v, par = stack.pop()
  for nv, c, d in T[v]:
    if nv == par:
      continue
    G[v].append((nv, c, d))
    edge[v].append(nv)
    stack.append((nv, v))

seg = LCA(edge, 0)
A = [0]*q
C = [[] for _ in range(n)]
num = [0]*n
cum = [0]*n
for i in range(q):
  x, y, u, v = map(int, input().split())
  u -= 1
  v -= 1
  a = seg.query(u, v)
  C[u].append((i, x, y, 1))
  C[v].append((i, x, y, 1))
  C[a].append((i, x, y, -2))
dist = 0
stack = [0]
def dfs(v):
  global dist
  for i, x, y, b in C[v]:
    A[i] += (dist + num[x]*y - cum[x]) * b
  for nv, c, d in G[v]:
    dist += d
    num[c] += 1
    cum[c] += d
    dfs(nv)
    dist -= d
    num[c] -= 1
    cum[c] -= d
dfs(0)
print(*A, sep="\n")

Submission status: Accepted

Solution code:
def examA():
    N = DI()/dec(7)
    ans = N
    print(N)
    return

def examB():
    ans = 0
    print(ans)
    return

def examC():
    ans = 0
    print(ans)
    return

def examD():
    ans = 0
    print(ans)
    return

def examE():
    ans = 0
    print(ans)
    return

def examF():
    class LCA(object):
        def __init__(self, G, root=0):
            self.G = G
            self.root = root
            self.n = len(G)
            self.logn = (self.n - 1).bit_length()
            self.depth = [-1 if i != root else 0 for i in range(self.n)]
            self.parent = [[-1] * self.n for _ in range(self.logn)]
            self.W = [-1 if i != root else 0 for i in range(self.n)]
            self.dfs()
            self.doubling()
            # print(self.depth)
            # print(self.parent)
            # print(self.W)

        def dfs(self):
            que = [self.root]
            while que:
                u = que.pop()
                for v, (d, c) in self.G[u].items():
                    if self.depth[v] == -1:
                        self.depth[v] = self.depth[u] + 1
                        self.parent[0][v] = u
                        self.W[v] = self.W[u] + d
                        que += [v]

        def doubling(self):
            for i in range(1, self.logn):
                for v in range(self.n):
                    if self.parent[i - 1][v] != -1:
                        self.parent[i][v] = self.parent[i - 1][self.parent[i - 1][v]]

        def get(self, u, v):
            if self.depth[v] < self.depth[u]:
                u, v = v, u
            du = self.depth[u]
            dv = self.depth[v]
            for i in range(self.logn):  # depthの差分だけuを遡らせる
                if (dv - du) >> i & 1:
                    v = self.parent[i][v]
            if u == v: return u  # 高さ揃えた時点で一致してたら終わり
            for i in range(self.logn - 1, -1, -1):  # そうでなければ上から二分探索
                pu, pv = self.parent[i][u], self.parent[i][v]
                if pu != pv:
                    u, v = pu, pv
            return self.parent[0][u]

    # (参考) https://qiita.com/ophhdn/items/48710bfab29d1fdc4577
    def euler_tour(G, root=0):
        n = len(G)
        euler = []
        dq = deque([root])
        dq2 = deque()
        visited = [0] * n
        while dq:
            u = dq.pop()
            euler += [u]
            if visited[u]:
                continue
            for v in G[u].keys():
                if visited[v]:
                    dq += [v]
                # [親頂点、子頂点、子頂点、。。。]と入れていく.その後連結
                else:
                    dq2 += [v]
            dq.extend(dq2)
            dq2 = deque()
            visited[u] = 1
        return euler

    N, q = LI()
    V = [{} for _ in range(N)]
    for _ in range(N - 1):
        a, b, c, d = LI()
        V[a - 1][b - 1] = (d, c)
        V[b - 1][a - 1] = (d, c)
    lca = LCA(V)
    # クエリ先読み(しないと必要な色の情報O(n**2)とかいる)
    # クエリに関係あるのはu,vとlca頂点の3つ
    # 頂点uは色xを変えるクエリを持つ
    colors = [set() for _ in range(N)]
    Q = [LI()for _ in range(q)]
    for x, y, u, v in Q:
        u -= 1; v -= 1
        a = lca.get(u,v)
        colors[u].add(x)
        colors[v].add(x)
        colors[a].add(x)
    # オイラーツアー
    # 上記クエリで必要な値だけを、オイラーツアーで訪れたタイミングで取得する。
    ET = euler_tour(V)
    #print(ET)

    # クエリごとの根からの色の数、長さの合計を記録
    Q_color = [{}for _ in range(N)]
    Q_length = [{}for _ in range(N)]
    for color in colors[0]:
        Q_color[0][color] = 0
        Q_length[0][color] = 0

    # 色iが何個あるか
    S_color = defaultdict(int)
    # 色iの距離の合計
    S_length = defaultdict(int)

    visited = [False]*N
    visited[0] = True
    for i in range(len(ET)-1):
        now,ne = ET[i],ET[i+1]
        d,c = V[now][ne]
        # 帰りはマイナス
        if visited[ne]:
            S_color[c] -= 1
            S_length[c] -= d
            continue
        else:
            S_color[c] += 1
            S_length[c] += d

        for color in colors[ne]:
            Q_color[ne][color] = S_color[color]
            Q_length[ne][color] = S_length[color]

        visited[ne] = True

    ans = [0]*q
    for i,(x,y,u,v) in enumerate(Q):
        u -= 1; v -= 1
        a = lca.get(u, v)
        child_1 = lca.W[u] + (Q_color[u][x]*y - Q_length[u][x])
        child_2 = lca.W[v] + (Q_color[v][x]*y - Q_length[v][x])
        parent = lca.W[a] + (Q_color[a][x]*y - Q_length[a][x])
        #print(child_1,child_2,parent)

        ans[i] = child_1 + child_2 - parent * 2

    for v in ans:
        print(v)
    return


from decimal import getcontext,Decimal as dec
import sys,bisect,itertools,heapq,math,random
from copy import deepcopy
from heapq import heappop,heappush,heapify
from collections import Counter,defaultdict,deque
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
def I(): return int(input())
def LI(): return list(map(int,sys.stdin.readline().split()))
def DI(): return dec(input())
def LDI(): return list(map(dec,sys.stdin.readline().split()))
def LSI(): return list(map(str,sys.stdin.readline().split()))
def LS(): return sys.stdin.readline().split()
def SI(): return sys.stdin.readline().strip()
global mod,mod2,inf,alphabet,_ep
mod = 10**9 + 7
mod2 = 998244353
inf = 10**18
_ep = dec("0.000000000001")
alphabet = [chr(ord('a') + i) for i in range(26)]
alphabet_convert = {chr(ord('a') + i): i for i in range(26)}

getcontext().prec = 28

sys.setrecursionlimit(10**7)

if __name__ == '__main__':
    examF()

"""
142
12 9 1445 0 1
asd dfg hj o o
aidn
"""