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):

from collections import defaultdict,deque
from heapq import heappush, heappop
import sys
import math
import bisect
import random
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S(): return list(sys.stdin.readline())[:-1]
def IR(n):
    return [I() for i in range(n)]
def LIR(n):
    return [LI() for i in range(n)]
def SR(n):
    return [S() for i in range(n)]
def LSR(n):
    return [LS() for i in range(n)]

sys.setrecursionlimit(1000000)
mod = 1000000007


def A():
    n,a,b = LI()
    print(min(a*n,b))
    return


def B():
    n,d = LI()
    x = LIR(n)
    f = defaultdict(lambda : 0)
    for i in range(1000000):
        f[i*i] = 1
    ans = 0
    for i in range(n):
        for j in range(i+1,n):
            s = 0
            for k in range(d):
                s += (x[i][k]-x[j][k])**2
            if f[s]:
                ans += 1
    print(ans)
    return


def C():
    l,r = LI()
    if r-l > 2019:
        print(0)
        quit()
    ans = float("inf")
    for i in range(l,r+1):
        for j in range(i+1,r+1):
            if i*j%2019 < ans:
                ans = i*j%2019
    print(ans)
    return


def D():
    n = I()
    a = LI()
    for i in range(n):
        a[i] *= 2
    x = a[0]
    for i in range(1,n):
        if i%2:
            x -= a[i]
        else:
            x += a[i]
    b = [x//2]
    for i in range(n-1):
        b.append(abs(b[-1]-a[i]))
    print(*b)
    return


def E():
    n,k = LI()
    v = [[] for i in range(n)]
    for i in range(n-1):
        a,b = LI()
        a -= 1
        b -= 1
        v[a].append(b)
        v[b].append(a)
    if k == 1:
        if n == 1:
            print(1)
            quit()
        else:
            print(0)
            quit()
    if k == 2:
        print(2)
        quit()
    d = [0]*n
    v.append([])
    v.append([])
    q = deque([0])
    bfs = [1]*n
    bfs[0] = 0
    f = [0]*n
    while q:
        x= q.popleft()
        for y in v[x]:
            if bfs[y]:
                bfs[y] = 0
                q.append(y)
    ans = 1
    q = deque([0])
    dp = [None]*n
    dp[0] = k
    bfs = [1]*n
    bfs[0] = 0
    while q:
        x = q.popleft()
        m = len(v[x])
        for y in v[x]:
            if bfs[y]:
                bfs[y] = 0
                dp[y] = k-m
                m -= 1
                q.append(y)
    for i in dp:
        ans *= i
        ans %= mod
    print(ans)
    return


def F():
    def lca(x,y):
        k = depth[x]-depth[y]
        while k > 0:
            x = par[x][int(math.log(k,2))]
            k = depth[x]-depth[y]
        k = -k
        while k > 0:
            y = par[y][int(math.log(k,2))]
            k = depth[y]-depth[x]
        if x == y:
            return x
        for i in range(M+1)[::-1]:
            if i < len(par[x]):
                if par[x][i] != par[y][i]:
                    x = par[x][i]
                    y = par[y][i]
        return par[x][0]

    def euler_tour(x,check,color):
        for i,c,d,k in f[x]:
            if k:
                query[i] -= 2*(-color[c][0]+color[c][1]*d)
            else:
                query[i] += -color[c][0]+color[c][1]*d
        for y,c,d in v[x]:
            if not check[y]:
                check[y] = 1
                color[c][0] += d
                color[c][1] += 1
                euler_tour(y,check,color)
                check[y] = 0
                color[c][0] -= d
                color[c][1] -= 1

    M = 16 
    n,Q = LI()
    v = [[] for i in range(n)]
    for i in range(n-1):
        a,b,c,d = LI()
        a -= 1
        b -= 1
        c -= 1
        v[a].append((b,c,d))
        v[b].append((a,c,d))
    par = [[] for i in range(n)]
    dist = [-1]*n
    dist[0] = 0
    depth = [0]*n
    q = deque([0])
    while q:
        x = q.popleft()
        for y,c,d in v[x]:
            if dist[y] < 0:
                dist[y] = dist[x]+d
                depth[y] = depth[x]+1
                q.append(y)
                par[y].append(x)

    l = [i for i in range(n)]
    l.sort(key = lambda x:depth[x])
    for i in range(M):
        k = 1<<(i+1)
        for x in l[::-1]:
            if depth[x] < k:break
            par[x].append(par[par[x][i]][i])
    f = [[] for i in range(n)] 
    query = [0]*Q 
    for i in range(Q):
        x,y,a,b = LI()
        x -= 1
        a -= 1
        b -= 1
        f[a].append((i,x,y,0))
        f[b].append((i,x,y,0))
        l = lca(a,b)
        f[l].append((i,x,y,1))
        query[i] = dist[a]+dist[b]-2*dist[l]
    check = [0]*n
    check[0] = 1
    color = [[0,0] for i in range(n)] 
    euler_tour(0,check,color)
    for i in query:
        print(i)
    return



if __name__ == "__main__":
    F()

Solution (Python):

from collections import defaultdict,deque
from heapq import heappush, heappop
import sys
import math
import bisect
import random
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S(): return list(sys.stdin.readline())[:-1]
def IR(n):
    return [I() for i in range(n)]
def LIR(n):
    return [LI() for i in range(n)]
def SR(n):
    return [S() for i in range(n)]
def LSR(n):
    return [LS() for i in range(n)]

sys.setrecursionlimit(1000000)
mod = 1000000007


def A():
    n,a,b = LI()
    print(min(a*n,b))
    return


def B():
    n,d = LI()
    x = LIR(n)
    f = defaultdict(lambda : 0)
    for i in range(1000000):
        f[i*i] = 1
    ans = 0
    for i in range(n):
        for j in range(i+1,n):
            s = 0
            for k in range(d):
                s += (x[i][k]-x[j][k])**2
            if f[s]:
                ans += 1
    print(ans)
    return


def C():
    l,r = LI()
    if r-l > 2019:
        print(0)
        quit()
    ans = float("inf")
    for i in range(l,r+1):
        for j in range(i+1,r+1):
            if i*j%2019 < ans:
                ans = i*j%2019
    print(ans)
    return


def D():
    n = I()
    a = LI()
    for i in range(n):
        a[i] *= 2
    x = a[0]
    for i in range(1,n):
        if i%2:
            x -= a[i]
        else:
            x += a[i]
    b = [x//2]
    for i in range(n-1):
        b.append(abs(b[-1]-a[i]))
    print(*b)
    return


def E():
    n,k = LI()
    v = [[] for i in range(n)]
    for i in range(n-1):
        a,b = LI()
        a -= 1
        b -= 1
        v[a].append(b)
        v[b].append(a)
    if k == 1:
        if n == 1:
            print(1)
            quit()
        else:
            print(0)
            quit()
    if k == 2:
        print(2)
        quit()
    d = [0]*n
    v.append([])
    v.append([])
    q = deque([0])
    bfs = [1]*n
    bfs[0] = 0
    f = [0]*n
    while q:
        x= q.popleft()
        for y in v[x]:
            if bfs[y]:
                bfs[y] = 0
                q.append(y)
    ans = 1
    q = deque([0])
    dp = [None]*n
    dp[0] = k
    bfs = [1]*n
    bfs[0] = 0
    while q:
        x = q.popleft()
        m = len(v[x])
        for y in v[x]:
            if bfs[y]:
                bfs[y] = 0
                dp[y] = k-m
                m -= 1
                q.append(y)
    for i in dp:
        ans *= i
        ans %= mod
    print(ans)
    return


def F():
    def lca(x,y):
        k = depth[x]-depth[y]
        while k > 0:
            x = par[x][int(math.log(k,2))]
            k = depth[x]-depth[y]
        k = -k
        while k > 0:
            y = par[y][int(math.log(k,2))]
            k = depth[y]-depth[x]
        if x == y:
            return x
        for i in range(M+1)[::-1]:
            if i < len(par[x]):
                if par[x][i] != par[y][i]:
                    x = par[x][i]
                    y = par[y][i]
        return par[x][0]

    def euler_tour(x,check,color):
        for i,c,d,k in f[x]:
            if k:
                query[i] -= 2*(-color[c][0]+color[c][1]*d)
            else:
                query[i] += -color[c][0]+color[c][1]*d
        for y,c,d in v[x]:
            if not check[y]:
                check[y] = 1
                color[c][0] += d
                color[c][1] += 1
                euler_tour(y,check,color)
                check[y] = 0
                color[c][0] -= d
                color[c][1] -= 1

    M = 16 
    n,Q = LI()
    v = [[] for i in range(n)]
    for i in range(n-1):
        a,b,c,d = LI()
        a -= 1
        b -= 1
        c -= 1
        v[a].append((b,c,d))
        v[b].append((a,c,d))
    par = [[] for i in range(n)]
    par[0].append(0)
    dist = [-1]*n
    dist[0] = 0
    depth = [0]*n
    q = deque([0])
    while q:
        x = q.popleft()
        for y,c,d in v[x]:
            if dist[y] < 0:
                dist[y] = dist[x]+d
                depth[y] = depth[x]+1
                q.append(y)
                par[y].append(x)

    l = [i for i in range(n)]
    l.sort(key = lambda x:depth[x])
    for i in range(M):
        k = 1<<(i+1)
        for x in l[::-1]:
            if depth[x] < k:break
            par[x].append(par[par[x][i]][i])
    f = [[] for i in range(n)] 
    query = [0]*Q 
    for i in range(Q):
        x,y,a,b = LI()
        x -= 1
        a -= 1
        b -= 1
        f[a].append((i,x,y,0))
        f[b].append((i,x,y,0))
        l = lca(a,b)
        f[l].append((i,x,y,1))
        query[i] = dist[a]+dist[b]-2*dist[l]
    check = [0]*n
    check[0] = 1
    color = [[0,0] for i in range(n)] 
    euler_tour(0,check,color)
    for i in query:
        print(i)
    return



if __name__ == "__main__":
    F()

Solution (Python):

from collections import defaultdict,deque
from heapq import heappush, heappop
import sys
import math
import bisect
import random
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S(): return list(sys.stdin.readline())[:-1]
def IR(n):
    return [I() for i in range(n)]
def LIR(n):
    return [LI() for i in range(n)]
def SR(n):
    return [S() for i in range(n)]
def LSR(n):
    return [LS() for i in range(n)]

sys.setrecursionlimit(1000000)
mod = 1000000007


def A():
    n,a,b = LI()
    print(min(a*n,b))
    return


def B():
    n,d = LI()
    x = LIR(n)
    f = defaultdict(lambda : 0)
    for i in range(1000000):
        f[i*i] = 1
    ans = 0
    for i in range(n):
        for j in range(i+1,n):
            s = 0
            for k in range(d):
                s += (x[i][k]-x[j][k])**2
            if f[s]:
                ans += 1
    print(ans)
    return


def C():
    l,r = LI()
    if r-l > 2019:
        print(0)
        quit()
    ans = float("inf")
    for i in range(l,r+1):
        for j in range(i+1,r+1):
            if i*j%2019 < ans:
                ans = i*j%2019
    print(ans)
    return


def D():
    n = I()
    a = LI()
    for i in range(n):
        a[i] *= 2
    x = a[0]
    for i in range(1,n):
        if i%2:
            x -= a[i]
        else:
            x += a[i]
    b = [x//2]
    for i in range(n-1):
        b.append(abs(b[-1]-a[i]))
    print(*b)
    return


def E():
    n,k = LI()
    v = [[] for i in range(n)]
    for i in range(n-1):
        a,b = LI()
        a -= 1
        b -= 1
        v[a].append(b)
        v[b].append(a)
    if k == 1:
        if n == 1:
            print(1)
            quit()
        else:
            print(0)
            quit()
    if k == 2:
        print(2)
        quit()
    d = [0]*n
    v.append([])
    v.append([])
    q = deque([0])
    bfs = [1]*n
    bfs[0] = 0
    f = [0]*n
    while q:
        x= q.popleft()
        for y in v[x]:
            if bfs[y]:
                bfs[y] = 0
                q.append(y)
    ans = 1
    q = deque([0])
    dp = [None]*n
    dp[0] = k
    bfs = [1]*n
    bfs[0] = 0
    while q:
        x = q.popleft()
        m = len(v[x])
        for y in v[x]:
            if bfs[y]:
                bfs[y] = 0
                dp[y] = k-m
                m -= 1
                q.append(y)
    for i in dp:
        ans *= i
        ans %= mod
    print(ans)
    return


def F():
    def lca(x,y):
        k = depth[x]-depth[y]
        while k > 0:
            x = par[x][int(math.log(k,2))]
            k = depth[x]-depth[y]
        k = -k
        while k > 0:
            y = par[y][int(math.log(k,2))]
            k = depth[y]-depth[x]
        if x == y:
            return x
        for i in range(M+1)[::-1]:
            if par[x][i] != par[y][i]:
                x = par[x][i]
                y = par[y][i]
        return par[x][0]

    def euler_tour(x,check,color):
        for i,c,d,k in f[x]:
            if k:
                query[i] -= 2*(-color[c][0]+color[c][1]*d)
            else:
                query[i] += -color[c][0]+color[c][1]*d
        for y,c,d in v[x]:
            if not check[y]:
                check[y] = 1
                color[c][0] += d
                color[c][1] += 1
                euler_tour(y,check,color)
                check[y] = 0
                color[c][0] -= d
                color[c][1] -= 1

    M = 17 
    n,Q = LI()
    v = [[] for i in range(n)]
    for i in range(n-1):
        a,b,c,d = LI()
        a -= 1
        b -= 1
        c -= 1
        v[a].append((b,c,d))
        v[b].append((a,c,d))
    par = [[] for i in range(n)]
    par[0].append(0)
    dist = [-1]*n
    dist[0] = 0
    depth = [0]*n
    q = deque([0])
    while q:
        x = q.popleft()
        for y,c,d in v[x]:
            if dist[y] < 0:
                dist[y] = dist[x]+d
                depth[y] = depth[x]+1
                q.append(y)
                par[y].append(x)

    l = [i for i in range(n)]
    l.sort(key = lambda x:depth[x])
    for i in range(M):
        for x in l:
            par[x].append(par[par[x][i]][i])
    f = [[] for i in range(n)] 
    query = [0]*Q 
    for i in range(Q):
        x,y,a,b = LI()
        x -= 1
        a -= 1
        b -= 1
        f[a].append((i,x,y,0))
        f[b].append((i,x,y,0))
        l = lca(a,b)
        f[l].append((i,x,y,1))
        query[i] = dist[a]+dist[b]-2*dist[l]
    check = [0]*n
    check[0] = 1
    color = [[0,0] for i in range(n)] 
    euler_tour(0,check,color)
    for i in query:
        print(i)
    return



if __name__ == "__main__":
    F()

Solution (Python):
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**7)
import numpy as np

N,Q = map(int,input().split())
graph = [[] for _ in range(N+1)]
for _ in range(N-1):
    a,b,c,d = map(int,input().split())
    graph[a].append((b,c,d))
    graph[b].append((a,c,d))
query = [[int(x) for x in input().split()] for _ in range(Q)]

def euler_tour(x, tour_v, tour_d, depth = 0, parent=None):
    tour_v.append(x)
    tour_d.append(depth)
    for y, c, d in graph[x]:
        if y == parent:
            continue
        euler_tour(y, tour_v, tour_d, depth + 1, parent = x)
        tour_v.append(x)
        tour_d.append(depth)

tour_v = []
tour_d = []
euler_tour(1, tour_v, tour_d)
tour_d_arr = np.array(tour_d)
v_to_i = {v:i for i,v in enumerate(tour_v)}
v_to_d = dict(zip(tour_v, tour_d))



L = len(tour_v)
U = L.bit_length()
sp = [np.arange(L)]
for i in range(1,U):
    prev = sp[-1]
    width = 1 << (i-1)
    n1 = prev[:-width]
    n2 = prev[width:]
    sp.append(np.where(tour_d_arr[n1] < tour_d_arr[n2], n1, n2))

def LCA(x,y):
    ix = v_to_i[x]
    iy = v_to_i[y]
    if ix > iy:
        ix,iy = iy,ix
    items = iy - ix + 1
    L = items.bit_length() - 1
    n1 = sp[L][ix]
    n2 = sp[L][iy - (1 << L) + 1]
    n = n1 if tour_d[n1] < tour_d[n2] else n2
    return tour_v[n]

tasks = [[] for _ in range(N+1)]
for i,(x,y,u,v) in enumerate(query):
    tasks[u].append((i,x,y,1))
    tasks[v].append((i,x,y,1))
    tasks[LCA(u,v)].append((i,x,y,-2))

answer = [0] * Q

def dfs(x = 1, sums = [0] * (N+1), nums = [0] * (N+1), total = 0, parent = 0):
    for i,c,d,coef in tasks[x]:
        answer[i] += coef * (total - sums[c] + nums[c] * d)
    for y,c,d in graph[x]:
        if y == parent:
            continue
        sums[c] += d
        nums[c] += 1
        total += d
        dfs(y, sums, nums, total, x)
        sums[c] -= d
        nums[c] -= 1
        total -= d
    return

dfs()
print('\n'.join(map(str,answer)))

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

def process():
    INF = (N, None)
    M = 2*N
    M0 = 2**(M-1).bit_length()
    data = [INF]*(2*M0)
    lnc = [0]*N

    G = [[] for _ in range(N)]
    dp = {}
    for v in range(N-1):
        a, b, c, d = map(int, readline().split())
        a, b = a-1, b-1
        G[a].append(b)
        G[b].append(a)
        dp[(min(a,b), max(a,b))] = c, d

    S = [0]*(2*N)
    F = [0]*(2*N)
    stack = [0] + G[0][::-1]
    visited = set([0])
    depth = [0]*N
    depthh = [0]*N
    mmn = [[0] for _ in range(N)]
    msn = [[0] for _ in range(N)]
    iin = [[] for _ in range(N)]
    ccs = [0]*N
    path = [0]
    ii = 0
    d = 0
    dd = 0

    while True:
        if len(stack) == 0:
            break
        v = stack.pop()
        if v in visited:
            continue
        ii += 1
        if v >=0:
            visited.add(v)
            cc, dpd = dp[(min(v,path[-1]), max(v,path[-1]))]
            F[v] = ii
            S[ii] = v
            d += 1
            dd += dpd
            depth[v] = d
            depthh[v] = dd
            ccs[v] = cc

            mmn[cc].append(mmn[cc][-1]+1)
            msn[cc].append(msn[cc][-1]+dpd)
            iin[cc].append(v)

            path.append(v)
            stack += [-v] + G[v][::-1]
        else:
            cc, dpd = dp[(min(path[-1], path[-2]), max(path[-1],path[-2]))]
            dd -= dpd
            mmn[cc].append(mmn[cc][-1]-1)
            iin[cc].append(-path[-1])
            msn[cc].append(msn[cc][-1]-dpd)
            F[-path[-1]] = ii
            path.pop()
            S[ii] = path[-1]
            d -= 1
    
    for i, z in enumerate(mmn):
        lnc[i] = len(z)-1

    for i, v in enumerate(S):
        data[M0-1+i] = (depth[v], i)
    for i in range(M0-2, -1, -1):
        data[i] = min(data[2*i+1], data[2*i+2])

    for q in range(Q):
        x, y, u, v = map(int, readline().split())
        u, v = u-1, v-1
        fu = F[u]; fv = F[v]
        if fu > fv:
            fu, fv = fv, fu

        minx = INF
        a, b = fu, fv+1
        a += M0; b += M0
        while a < b:
            if b & 1:
                b -= 1
                minx = min(minx, data[b-1])
            if a & 1:
                minx = min(minx, data[a-1])
                a += 1
            a >>= 1; b >>= 1
        cc = S[minx[1]]
        if lnc[x] == 0:
            diff = 0
        else:
            ll, mm, ms, lncc = iin[x], mmn[x], msn[x], lnc[x]-1
            uvcs = []
            for target_i in [F[u], F[v], F[cc]]:
                ind, lw, hw =  (lnc[x]-1)//2, 0, lnc[x]-1
                if target_i < F[ll[0]] or target_i >= F[ll[lncc]]:
                    uvcs.append((0,0))
                else:
                    while True:
                        if F[ll[ind]] <= target_i:
                            if target_i < F[ll[ind+1]]:
                                uvcs.append((mm[ind+1], ms[ind+1]))
                                break
                            ind, lw = (ind+1 + hw)//2, ind+1
                            continue
                        ind, hw = (ind-1 + lw)//2, ind-1
            diff = (uvcs[0][0] + uvcs[1][0] - 2 * uvcs[2][0]) * y - (uvcs[0][1] + uvcs[1][1] - 2 * uvcs[2][1])
        print(depthh[u] + depthh[v] - 2*depthh[cc] + diff)

if __name__ == '__main__':
    process()

Solution (Python):
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**7)
from collections import defaultdict

N,Q = map(int,input().split())
graph = [[] for _ in range(N+1)]
for _ in range(N-1):
    a,b,c,d = map(int,input().split())
    graph[a].append((b,c,d))
    graph[b].append((a,c,d))
query = [[int(x) for x in input().split()] for _ in range(Q)]

depth = [0] * (N+1)
U = 17
ancestor = [[0] * (U+1) for _ in range(N+1)] 

q = [(1,0,0)]
while q:
    qq = []
    for x,d,parent in q:
        depth[x] = d
        ax = ancestor[x]
        ax[0] = parent
        for i in range(d.bit_length() - 1):
            ax[i+1] = ancestor[ax[i]][i]
        for y, _, _ in graph[x]:
            if y == parent:
                continue
            qq.append((y, d+1, x))
    q = qq

def LCA(x,y):
    dx = depth[x]
    dy = depth[y]
    if dx > dy:
        x,y = y,x
        dx,dy = dy,dx
    diff = dy - dx
    while diff:
        step = diff & (-diff)
        y = ancestor[y][step.bit_length() - 1]
        diff -= step
    while x != y:
        j = 0
        while ancestor[x][j] != ancestor[y][j]:
            j += 1
        if j == 0:
            return ancestor[x][0]
        x = ancestor[x][j-1]
        y = ancestor[y][j-1]
    return x

tasks = [[] for _ in range(N+1)]
for i,(x,y,u,v) in enumerate(query):
    tasks[u].append((i,x,y,1))
    tasks[v].append((i,x,y,1))
    tasks[LCA(u,v)].append((i,x,y,-2))

answer = [0] * Q

def dfs(x = 1, sums = [0] * (N+1), nums = [0] * (N+1), total = 0, parent = 0):
    for i,c,d,coef in tasks[x]:
        answer[i] += coef * (total - sums[c] + nums[c] * d)
    for y,c,d in graph[x]:
        if y == parent:
            continue
        sums[c] += d
        nums[c] += 1
        total += d
        dfs(y, sums, nums, total, x)
        sums[c] -= d
        nums[c] -= 1
        total -= d
    return

dfs()

print('\n'.join(map(str,answer)))

Solution (Python):
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**7)
from collections import defaultdict

N,Q = map(int,input().split())
graph = [[] for _ in range(N+1)]
for _ in range(N-1):
    a,b,c,d = map(int,input().split())
    graph[a].append((b,c,d))
    graph[b].append((a,c,d))
query = [[int(x) for x in input().split()] for _ in range(Q)]

def set_ancestor(x=1, d=0, parent=0):
    depth[x] = d
    ax = ancestor[x]
    ax[0] = parent
    for i in range(d.bit_length() - 1):
        ax[i+1] = ancestor[ax[i]][i]
    for y, _, _ in graph[x]:
        if y == parent:
            continue
        set_ancestor(y, d+1, x)

depth = [0] * (N+1)
U = 17
ancestor = [[0] * (U+1) for _ in range(N+1)] 
set_ancestor()

def LCA(x,y):
    dx = depth[x]
    dy = depth[y]
    if dx > dy:
        x,y = y,x
        dx,dy = dy,dx
    diff = dy - dx
    while diff:
        step = diff & (-diff)
        y = ancestor[y][step.bit_length() - 1]
        diff -= step
    while x != y:
        j = 0
        while ancestor[x][j] != ancestor[y][j]:
            j += 1
        if j == 0:
            return ancestor[x][0]
        x = ancestor[x][j-1]
        y = ancestor[y][j-1]
    return x

tasks = [[] for _ in range(N+1)]
for i,(x,y,u,v) in enumerate(query):
    tasks[u].append((i,x,y,1))
    tasks[v].append((i,x,y,1))
    tasks[LCA(u,v)].append((i,x,y,-2))

answer = [0] * Q

def dfs(x = 1, sums = [0] * (N+1), nums = [0] * (N+1), total = 0, parent = 0):
    for i,c,d,coef in tasks[x]:
        answer[i] += coef * (total - sums[c] + nums[c] * d)
    for y,c,d in graph[x]:
        if y == parent:
            continue
        sums[c] += d
        nums[c] += 1
        total += d
        dfs(y, sums, nums, total, x)
        sums[c] -= d
        nums[c] -= 1
        total -= d
    return

dfs()

print('\n'.join(map(str,answer)))

Solution (Python):
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**7)
from collections import defaultdict

N,Q = map(int,input().split())
graph = [[] for _ in range(N+1)]
for _ in range(N-1):
    a,b,c,d = map(int,input().split())
    graph[a].append((b,c,d))
    graph[b].append((a,c,d))
query = [[int(x) for x in input().split()] for _ in range(Q)]

def set_ancestor(x=1, d=0, parent=0):
    depth[x] = d
    ax = ancestor[x]
    ax[0] = parent
    for i in range(d.bit_length() - 1):
        ax[i+1] = ancestor[ax[i]][i]
    for y, _, _ in graph[x]:
        if y == parent:
            continue
        set_ancestor(y, d+1, x)

depth = [0] * (N+1)
U = 17
ancestor = [[0] * (U+1) for _ in range(N+1)] 
set_ancestor()

def LCA(x,y):
    dx = depth[x]
    dy = depth[y]
    if dx > dy:
        x,y = y,x
        dx,dy = dy,dx
    diff = dy - dx
    while diff:
        step = diff & (-diff)
        y = ancestor[y][step.bit_length() - 1]
        diff -= step
    while x != y:
        j = 0
        while ancestor[x][j] != ancestor[y][j]:
            j += 1
        if j == 0:
            return ancestor[x][0]
        x = ancestor[x][j-1]
        y = ancestor[y][j-1]
    return x

tasks = [[] for _ in range(N+1)]
for i,(x,y,u,v) in enumerate(query):
    tasks[u].append((i,x,y,1))
    tasks[v].append((i,x,y,1))
    tasks[LCA(u,v)].append((i,x,y,-2))

answer = [0] * Q

def dfs(x, sums = defaultdict(int), nums = defaultdict(int), total = 0, parent = 0):
    for i,c,d,coef in tasks[x]:
        answer[i] += coef * (total - sums[c] + nums[c] * d)
    for y,c,d in graph[x]:
        if y == parent:
            continue
        sums[c] += d
        nums[c] += 1
        total += d
        dfs(y, sums, nums, total, x)
        sums[c] -= d
        nums[c] -= 1
        total -= d
    return

dfs(1)

print('\n'.join(map(str,answer)))

Solution (Python):
from collections import deque,defaultdict
import sys
sys.setrecursionlimit(10**7)
N,Q=map(int,input().split())
table=[[] for i in range(N)]
ddcost=defaultdict(tuple)
for i in range(N-1):
    a,b,c,d=map(int,input().split())
    a,b,c=a-1,b-1,c-1
    table[a].append(b)
    table[b].append(a)
    ddcost[(min(a,b),max(b,a))]=(c,d)


H=deque()
H.append(0)
visit=[-1]*N
visit[0]=0
parent=[[-1]*N for i in range(18)]
while H:
    x=H.popleft()
    for y in table[x]:
        if visit[y]!=-1:
            continue
        parent[0][y]=x
        visit[y]=visit[x]+1
        H.append(y)
for k in range(17):
    for i in range(N):
        if parent[k][i]<0:
            parent[k+1][i]=-1
        else:
            parent[k + 1][i]=parent[k][parent[k][i]]
def lca(u,v):
    if visit[u]>visit[v]:
        u,v=v,u
    for k in range(18):
        if ((visit[v]-visit[u] )>>k)&1:
            v=parent[k][v]
    if u==v:
        return u
    for k in range(17,-1,-1):
        if parent[k][u]!=parent[k][v]:
            u=parent[k][u]
            v=parent[k][v]
    return parent[0][u]

query=[]
sakidori=[set() for i in range(N)]
for i in range(Q):
    x,y,u,v=map(int,input().split())
    x,u,v=x-1,u-1,v-1
    if u>=v:
        u,v=v,u
    pa=lca(u,v)
    sakidori[u].add(x)
    sakidori[v].add(x)
    sakidori[pa].add(x)
    query.append((x,y,u,v,pa))
ddcolorsum=defaultdict(int)
ddcolornum=defaultdict(int)
W=deque()
colorsum=[0]*(N)
colornum=[0]*(N)
dist=[0]*N
vi=[0]*N
W.append((0,0,1))

while W:
    
    pa,ci,vector=W.pop()
    if vector==-1:
        color,dis=ddcost[(min(pa,ci),max(pa,ci))]
        colorsum[color]-=dis
        colornum[color]-=1
        
        continue
    if pa==0 and ci==0:
        for y in table[ci]:
            W.append((ci, y, 1))
        for co in sakidori[0]:
            ddcolorsum[(0,co)]=0
            ddcolornum[(0,co)]=0
        continue
    color,dis=ddcost[(min(pa,ci),max(pa,ci))]
    dist[ci]=dist[pa]+dis
    colorsum[color]+=dis
    colornum[color]+=1
    for co in sakidori[ci]:
        ddcolorsum[(ci, co)] = colorsum[co]
        ddcolornum[(ci, co)] = colornum[co]
    
    W.append((pa,ci,-1))
    for y in table[ci]:
        if y==pa:
            continue
        W.append((ci,y,1))



def dista(x,y,u):
    return dist[u]-ddcolorsum[(u,x)]+y*ddcolornum[(u,x)]
for x,y,u,v,pa in query:
    
    
    print(dista(x,y,u)+dista(x,y,v)-2*dista(x,y,pa))