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: Time Limit Exceeded

Solution code:
import sys
sys.setrecursionlimit(1000000)

from bisect import bisect_right as br
N, K = map(int, input().split())
X = [[] for i in range(N)]
for i in range(N-1):
    x, y, c, d = map(int, input().split())
    X[x-1].append((y-1, c-1, d))
    X[y-1].append((x-1, c-1, d))

P = [(-1, 0, 0)] * N
Q = [0]
R = []
ET = []
done = [0] * N
ct = 0
CT = [0] * (N-1) * 2
CTA = [-1]* N
BT = [[[-1], [0], [0]] for _ in range(N)] # id, cnt, sum
# BT = [[] for _ in range(N)] # id, cnt, sum
# BT = [[-1]*N] + [[0]*N] + [[0]*N]
def dfs(i):
    global ct
    if done[i]:
        return 0
    R.append(i)
    done[i] = 1
    for a, c, d in X[i]:
        if a != P[i][0]:
            ET.append((i, a))
            P[a] = (i, c, d)
            for k in range(len(X[a])):
                if X[a][k][0] == i:
                    del X[a][k]
                    break
            # print(i, "->", a)
            if CTA[a] < 0: CTA[a] = ct
            BT[c][0].append(ct)
            BT[c][1].append(BT[c][1][-1]+1)
            BT[c][2].append(BT[c][2][-1]+d)
            ct += 1
            dfs(a)
            BT[c][0].append(ct)
            BT[c][1].append(BT[c][1][-1]-1)
            BT[c][2].append(BT[c][2][-1]-d)
            ct += 1
            # print(a, "->", i)

dfs(0)
L = [[0, 0] for _ in range(N)] # depth, dist, list
# print("BT =", BT)
# print("CTA =", CTA)

for i in R[1:]:
    p, c, d = P[i]
    L[i][0] = L[p][0] + 1
    L[i][1] = L[p][1] + d

D = [[P[i][0] for i in range(N)]] + [[-1]*N for _ in range(16)]
for k in range(1, 17):
    for i in range(N):
        a = D[k-1][i]
        if a > 0:
            D[k][i] = D[k-1][a]

def lca(u0, v0):
    u, v = u0, v0
    if L[u][0] < L[v][0]:
        u, v = v, u
    
    while L[u][0] > L[v][0]:
        d = L[u][0] - L[v][0]
        dd = d.bit_length() - 1
        u = D[dd][u]
    if u == v:
        return u
    
    for i in range(17)[::-1]:
        if D[i][u] != D[i][v]:
            u = D[i][u]
            v = D[i][v]
    
    return D[0][u]
    

def calc(x, y, w):
    # print("calc ", x, y, w)
    aa = br(BT[x][0], CTA[w]) - 1
        
    # print("aa =", aa)
    # print("BT =", BT)
    c = BT[x][1][aa]
    d = BT[x][2][aa]
    # print(x, y, w, aa, c, d, L[w][1])
    return L[w][1] + c*y - d

for _ in range(K):
    x, y, u, v = map(int, input().split())
    x, u, v = x-1, u-1, v-1
    
    ll = lca(u, v)
    print(calc(x, y, u) + calc(x, y, v) - 2*calc(x, y, ll))
    # print(calc(x, y, u, v))

Submission status: Time Limit Exceeded

Solution code:
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**6)
from bisect import bisect_right as br

N, K = map(int, input().split())
X = [[] for i in range(N)]
for i in range(N-1):
    x, y, c, d = map(int, input().split())
    X[x-1].append((y-1, c-1, d))
    X[y-1].append((x-1, c-1, d))

P = [(-1, 0, 0)] * N
Q = [0]
R = []
ET = []
done = [0] * N
ct = 0
CT = [0] * (N-1) * 2
CTA = [-1]* N
BT = [[[-1], [0], [0]] for _ in range(N)] # id, cnt, sum
# BT = [[] for _ in range(N)] # id, cnt, sum
# BT = [[-1]*N] + [[0]*N] + [[0]*N]
def dfs(i):
    global ct
    if done[i]:
        return 0
    R.append(i)
    done[i] = 1
    for a, c, d in X[i]:
        if a != P[i][0]:
            ET.append((i, a))
            P[a] = (i, c, d)
            for k in range(len(X[a])):
                if X[a][k][0] == i:
                    del X[a][k]
                    break
            # print(i, "->", a)
            if CTA[a] < 0: CTA[a] = ct
            BT[c][0].append(ct)
            BT[c][1].append(BT[c][1][-1]+1)
            BT[c][2].append(BT[c][2][-1]+d)
            ct += 1
            dfs(a)
            BT[c][0].append(ct)
            BT[c][1].append(BT[c][1][-1]-1)
            BT[c][2].append(BT[c][2][-1]-d)
            ct += 1
            # print(a, "->", i)

dfs(0)
L = [[0, 0] for _ in range(N)] # depth, dist, list
# print("BT =", BT)
# print("CTA =", CTA)

for i in R[1:]:
    p, c, d = P[i]
    L[i][0] = L[p][0] + 1
    L[i][1] = L[p][1] + d

D = [[P[i][0] for i in range(N)]] + [[-1]*N for _ in range(16)]
for k in range(1, 17):
    for i in range(N):
        a = D[k-1][i]
        if a > 0:
            D[k][i] = D[k-1][a]


def lca(u0, v0):
    u, v = u0, v0
    if L[u][0] < L[v][0]:
        u, v = v, u
    
    while L[u][0] > L[v][0]:
        d = L[u][0] - L[v][0]
        dd = d.bit_length() - 1
        u = D[dd][u]
    if u == v:
        return u
    
    for i in range(17)[::-1]:
        if D[i][u] != D[i][v]:
            u = D[i][u]
            v = D[i][v]
    
    return D[0][u]
    

def calc(x, y, w):
    # print("calc ", x, y, w)
    aa = br(BT[x][0], CTA[w]) - 1
        
    # print("aa =", aa)
    # print("BT =", BT)
    c = BT[x][1][aa]
    d = BT[x][2][aa]
    # print(x, y, w, aa, c, d, L[w][1])
    return L[w][1]+c*y-d

for _ in range(K):
    x, y, u, v = map(int, input().split())
    x, u, v = x-1, u-1, v-1
    
    ll = lca(u, v)
    print(calc(x, y, u)+calc(x, y, v)-2*calc(x, y, ll))
    # print(calc(x, y, u, v))

Submission status: Time Limit Exceeded

Solution code:
import sys
from collections import defaultdict
from itertools import accumulate
sys.setrecursionlimit(10**7)
 
 
N, Q = map(int, input().split())
G = [[] for _ in range(N)]
dp = {}

for v in range(N-1):
    a, b, c, d = map(int, input().split())
    a, b = a-1, b-1
    G[a].append(b)
    G[b].append(a)
    dp["{}-{}".format(min(a,b), max(a,b))] = c, d
 
S = []
F = [0]*N
depth = [0]*N
depthh = [0]*N
vn = [[] for _ in range(N)]
sn = [[] for _ in range(N)]
iin = [[] for _ in range(N)]
w2i = [0]*(2*N)
ii = 0
def dfs(bb, v, d, dd, cc, dpd):
    global ii
    F[v] = len(S)
    depth[v] = d
    depthh[v] = dd
    S.append(v)
    vn[cc].append(1)
    sn[cc].append(dpd)
    iin[cc].append(v)
    w2i[v] = ii
    ii += 1
    for w in G[v]:
        if w == bb:
            continue
        nvn, dpd = dp["{}-{}".format(min(v,w), max(v,w))]
        dfs(v, w, d+1, dd+dpd, nvn, dpd)
        S.append(v)
        vn[nvn].append(-1)
        sn[nvn].append(-dpd)
        iin[nvn].append(-w)
        w2i[-w] = ii
        ii += 1

dfs(None, 0, 0, 0, 0,0)
mmn = []
lnc = []
for vvv in vn:
    lnc.append(len(vvv))
    mmn.append(list(accumulate(vvv)))
msn = []
for vvv in sn:
    msn.append(list(accumulate(vvv)))
 
INF = (N, None)
 
M = 2*N
M0 = 2**(M-1).bit_length()
data = [INF]*(2*M0)
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])
 
def _query(a, b):
    yield INF
    a += M0; b += M0
    while a < b:
        if b & 1:
            b -= 1
            yield data[b-1]
        if a & 1:
            yield data[a-1]
            a += 1
        a >>= 1; b >>= 1
 
def query(u, v):
    fu = F[u]; fv = F[v]
    if fu > fv:
        fu, fv = fv, fu
    return S[min(_query(fu, fv+1))[1]]

def b_s(ll, mm, ms, ind, lw, hw, target_i, lncc):
    if target_i < w2i[ll[0]]:
        return 0, 0
    if target_i >= w2i[ll[lncc]]:
        return 0, 0
    while True:
        if w2i[ll[ind]] <= target_i:
            if target_i < w2i[ll[ind+1]]:
                return (mm[ind], ms[ind])
            ind, lw = (ind+1 + hw)//2, ind+1
            continue
        else:
            ind, hw = (ind-1 + lw)//2, ind-1

def iro(u, v, cc, x, y):
    u_n, u_d = b_s(iin[x], mmn[x], msn[x], (lnc[x]-1)//2, 0, lnc[x]-1, w2i[u], lnc[x]-1)
    v_n, v_d = b_s(iin[x], mmn[x], msn[x], (lnc[x]-1)//2, 0, lnc[x]-1, w2i[v], lnc[x]-1)
    c_n, c_d = b_s(iin[x], mmn[x], msn[x], (lnc[x]-1)//2, 0, lnc[x]-1, w2i[cc], lnc[x]-1)
    return (u_n + v_n - 2 * (c_n)) * y - (u_d + v_d - 2 * (c_d))

for q in range(Q):
    x, y, u, v = map(int, input().split())
    u, v = u-1, v-1
    cc = query(u, v)
    diff = 0
    if lnc[x] == 0:
        diff = 0
    else:
        diff = iro(u, v, cc, x, y)
    print(depthh[u] + depthh[v] - 2*depthh[cc] + diff)

Submission status: Time Limit Exceeded

Solution code:
import sys
from collections import defaultdict
from itertools import accumulate
sys.setrecursionlimit(10**7)
 
readline = sys.stdin.readline
write = sys.stdout.write
 
N, Q = map(int, readline().split())
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["{}-{}".format(min(a,b), max(a,b))] = c, d
 
S = []
F = [0]*N
depth = [0]*N
depthh = [0]*N
vn = [[] for _ in range(N)]
sn = [[] for _ in range(N)]
iin = [[] for _ in range(N)]
w2i = [0]*(2*N)

ii = 0
def dfs(bb, v, d, dd, cc, dpd):
    global ii
    F[v] = len(S)
    depth[v] = d
    depthh[v] = dd
    S.append(v)
    vn[cc].append(1)
    sn[cc].append(dpd)
    iin[cc].append(v)
    w2i[v] = ii
    ii += 1
    for w in G[v]:
        if w == bb:
            continue
        nvn, dpd = dp["{}-{}".format(min(v,w), max(v,w))]
        dfs(v, w, d+1, dd+dpd, nvn, dpd)
        S.append(v)
        vn[nvn].append(-1)
        sn[nvn].append(-dpd)
        iin[nvn].append(-w)
        w2i[-w] = ii
        ii += 1

dfs(None, 0, 0, 0, 0,0)
mmn = []
lnc = []
for vvv in vn:
    lnc.append(len(vvv))
    mmn.append(list(accumulate(vvv)))
msn = []
for vvv in sn:
    msn.append(list(accumulate(vvv)))
 
INF = (N, None)
 
M = 2*N
M0 = 2**(M-1).bit_length()
data = [INF]*(2*M0)
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])
 
def _query(a, b):
    yield INF
    a += M0; b += M0
    while a < b:
        if b & 1:
            b -= 1
            yield data[b-1]
        if a & 1:
            yield data[a-1]
            a += 1
        a >>= 1; b >>= 1
 
def query(u, v):
    fu = F[u]; fv = F[v]
    if fu > fv:
        fu, fv = fv, fu
    return S[min(_query(fu, fv+1))[1]]

def b_s(ll, mm, ms, ind, lw, hw, target_i, lncc):
    while True:
        if w2i[ll[ind]] <= target_i:
            if ind+1 >= len(ll):
                return 0, 0
            if target_i < w2i[ll[ind+1]]:
                return (mm[ind], ms[ind])
            ind, lw = (ind+1 + hw)//2, ind+1
            continue
        elif w2i[ll[ind]] > target_i:
            ind, hw = (ind-1 + lw)//2, ind-1
            continue

def iro(u, v, cc, x, y):
    if w2i[u] < w2i[iin[x][0]]:
        u_n, u_d = 0, 0
    else:
        u_n, u_d = b_s(iin[x], mmn[x], msn[x], (lnc[x]-1)//2, 0, lnc[x]-1, w2i[u], lnc[x]-1)
    if w2i[v] < w2i[iin[x][0]]:
        v_n, v_d = 0, 0
    else:
        v_n, v_d = b_s(iin[x], mmn[x], msn[x], (lnc[x]-1)//2, 0, lnc[x]-1, w2i[v], lnc[x]-1)
    if w2i[cc] < w2i[iin[x][0]]:
        c_n, c_d = 0, 0
    else:
        c_n, c_d = b_s(iin[x], mmn[x], msn[x], (lnc[x]-1)//2, 0, lnc[x]-1, w2i[cc], lnc[x]-1)
    return (u_n + v_n - 2 * (c_n)) * y - (u_d + v_d - 2 * (c_d))

for q in range(Q):
    x, y, u, v = map(int, readline().split())
    u, v = u-1, v-1
    cc = query(u, v)
    diff = 0
    if lnc[x] == 0:
        diff = 0
    else:
        diff = iro(u, v, cc, x, y)
    print(depthh[u] + depthh[v] - 2*depthh[cc] + diff)

Submission status: Time Limit Exceeded

Solution code:
import sys
from collections import defaultdict
from itertools import accumulate
sys.setrecursionlimit(10**7)
 
readline = sys.stdin.readline
write = sys.stdout.write
 
N, Q = map(int, readline().split())
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["{}-{}".format(min(a,b), max(a,b))] = c, d
 
S = []
F = [0]*N
depth = [0]*N
depthh = [0]*N
vn = [[] for _ in range(N)]
sn = [[] for _ in range(N)]
iin = [[] for _ in range(N)]
w2i = [0]*(2*N)

ii = 0
def dfs(bb, v, d, dd, cc, dpd):
    global ii
    F[v] = len(S)
    depth[v] = d
    depthh[v] = dd
    S.append(v)
    vn[cc].append(1)
    sn[cc].append(dpd)
    iin[cc].append(v)
    w2i[v] = ii
    ii += 1
    for w in G[v]:
        if w == bb:
            continue
        nvn, dpd = dp["{}-{}".format(min(v,w), max(v,w))]
        dfs(v, w, d+1, dd+dpd, nvn, dpd)
        S.append(v)
        vn[nvn].append(-1)
        sn[nvn].append(-dpd)
        iin[nvn].append(-w)
        w2i[-w] = ii
        ii += 1

dfs(None, 0, 0, 0, 0,0)
mmn = []
lnc = []
for vvv in vn:
    lnc.append(len(vvv))
    mmn.append(list(accumulate(vvv)))
msn = []
for vvv in sn:
    msn.append(list(accumulate(vvv)))
 
INF = (N, None)
 
M = 2*N
M0 = 2**(M-1).bit_length()
data = [INF]*(2*M0)
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])
 
def _query(a, b):
    yield INF
    a += M0; b += M0
    while a < b:
        if b & 1:
            b -= 1
            yield data[b-1]
        if a & 1:
            yield data[a-1]
            a += 1
        a >>= 1; b >>= 1
 
def query(u, v):
    fu = F[u]; fv = F[v]
    if fu > fv:
        fu, fv = fv, fu
    return S[min(_query(fu, fv+1))[1]]

def b_s(ll, mm, ms, ind, lw, hw, target_i, lncc):
    if w2i[ll[ind]] <= target_i:
        if ind+1 >= len(ll):
            return 0, 0
        if target_i < w2i[ll[ind+1]]:
            return (mm[ind], ms[ind])
        return b_s(ll, mm, ms, (ind+1 + hw)//2, ind+1, hw, target_i, lncc)
    elif w2i[ll[ind]] > target_i:
        return b_s(ll, mm, ms, (ind + lw)//2, lw, ind-1, target_i, lncc)
    return 0, 0

def iro(u, v, cc, x, y):
    if w2i[u] < w2i[iin[x][0]]:
        u_n, u_d = 0, 0
    else:
        u_n, u_d = b_s(iin[x], mmn[x], msn[x], (lnc[x]-1)//2, 0, lnc[x]-1, w2i[u], lnc[x]-1)
    if w2i[v] < w2i[iin[x][0]]:
        v_n, v_d = 0, 0
    else:
        v_n, v_d = b_s(iin[x], mmn[x], msn[x], (lnc[x]-1)//2, 0, lnc[x]-1, w2i[v], lnc[x]-1)
    if w2i[cc] < w2i[iin[x][0]]:
        c_n, c_d = 0, 0
    else:
        c_n, c_d = b_s(iin[x], mmn[x], msn[x], (lnc[x]-1)//2, 0, lnc[x]-1, w2i[cc], lnc[x]-1)
    return (u_n + v_n - 2 * (c_n)) * y - (u_d + v_d - 2 * (c_d))

for q in range(Q):
    x, y, u, v = map(int, readline().split())
    u, v = u-1, v-1
    cc = query(u, v)
    diff = 0
    if lnc[x] == 0:
        diff = 0
    else:
        diff = iro(u, v, cc, x, y)
    print(depthh[u] + depthh[v] - 2*depthh[cc] + diff)

Submission status: Time Limit Exceeded

Solution code:
import sys
from collections import defaultdict
from itertools import accumulate
sys.setrecursionlimit(10**7)
 
readline = sys.stdin.readline
write = sys.stdout.write
 
N, Q = map(int, readline().split())
G = [[] for _ in range(N)]
g = defaultdict(list)
dp = {}
cdd = {}

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["{}-{}".format(min(a,b), max(a,b))] = d
    cdd["{}-{}".format(min(a,b), max(a,b))] = c
cc = set()
i = 0
imkr = set()
while True:
    cc.add(i)
    for vv in g[i]:
        if vv not in cc:
            G[i].append(vv)
            imkr.add(vv)
    if len(imkr) == 0:
        break
    i = imkr.pop()
 
S = []
F = [0]*N
depth = [0]*N
depthh = [0]*N
vn = [[] for _ in range(N)]
sn = [[] for _ in range(N)]
iin = [[] for _ in range(N)]
aii = []
w2i = [0]*(2*N)

ii = 0
def dfs(bb, v, d, dd, cc, dpd):
    global ii
    F[v] = len(S)
    depth[v] = d
    depthh[v] = dd
    S.append(v)
    vn[cc].append(1)
    sn[cc].append(dpd)
    iin[cc].append(v)
    w2i[v] = ii
    ii += 1
    for w in G[v]:
        nvn = cdd["{}-{}".format(min(v,w), max(v,w))]
        dpd = dp["{}-{}".format(min(v,w), max(v,w))]
        dfs(v, w, d+1, dd+dpd, nvn, dpd)
        S.append(v)
        vn[nvn].append(-1)
        sn[nvn].append(-dpd)
        iin[nvn].append(-w)
        w2i[-w] = ii
        ii += 1

dfs(None, 0, 0, 0, 0,0)
mmn = []
lnc = []
for vvv in vn:
    lnc.append(len(vvv))
    mmn.append(list(accumulate(vvv)))
msn = []
for vvv in sn:
    msn.append(list(accumulate(vvv)))
 
INF = (N, None)
 
M = 2*N
M0 = 2**(M-1).bit_length()
data = [INF]*(2*M0)
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])
 
def _query(a, b):
    yield INF
    a += M0; b += M0
    while a < b:
        if b & 1:
            b -= 1
            yield data[b-1]
        if a & 1:
            yield data[a-1]
            a += 1
        a >>= 1; b >>= 1
 
def query(u, v):
    fu = F[u]; fv = F[v]
    if fu > fv:
        fu, fv = fv, fu
    return S[min(_query(fu, fv+1))[1]]

def b_s(ll, mm, ms, ind, lw, hw, target_i, lncc):
    if w2i[ll[ind]] <= target_i:
        if ind+1 >= len(ll):
            return 0, 0
        if target_i < w2i[ll[ind+1]]:
            return (mm[ind], ms[ind])
        return b_s(ll, mm, ms, (ind+1 + hw)//2, ind+1, hw, target_i, lncc)
    elif w2i[ll[ind]] > target_i:
        return b_s(ll, mm, ms, (ind + lw)//2, lw, ind-1, target_i, lncc)
    return 0, 0

def iro(u, v, cc, x, y):
    if w2i[u] < w2i[iin[x][0]]:
        u_n, u_d = 0, 0
    else:
        u_n, u_d = b_s(iin[x], mmn[x], msn[x], (lnc[x]-1)//2, 0, lnc[x]-1, w2i[u], lnc[x]-1)
    if w2i[v] < w2i[iin[x][0]]:
        v_n, v_d = 0, 0
    else:
        v_n, v_d = b_s(iin[x], mmn[x], msn[x], (lnc[x]-1)//2, 0, lnc[x]-1, w2i[v], lnc[x]-1)
    if w2i[cc] < w2i[iin[x][0]]:
        c_n, c_d = 0, 0
    else:
        c_n, c_d = b_s(iin[x], mmn[x], msn[x], (lnc[x]-1)//2, 0, lnc[x]-1, w2i[cc], lnc[x]-1)
    return (u_n + v_n - 2 * (c_n)) * y - (u_d + v_d - 2 * (c_d))

 
 
for q in range(Q):
    x, y, u, v = map(int, readline().split())
    u, v = u-1, v-1
    cc = query(u, v)
    diff = 0
    if lnc[x] == 0:
        diff = 0
    else:
        diff = iro(u, v, cc, x, y)
    print(depthh[u] + depthh[v] - 2*depthh[cc] + diff)

Submission status: Time Limit Exceeded

Solution code:
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))

Submission status: Time Limit Exceeded

Solution code:
import sys
from collections import defaultdict
sys.setrecursionlimit(10**7)
 
readline = sys.stdin.readline
write = sys.stdout.write
 
N, Q = map(int, readline().split())
G = [[] for _ in range(N)]
g = defaultdict(list)
dp = {}
cdd = {}

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["{}-{}".format(min(a,b), max(a,b))] = d
    cdd["{}-{}".format(min(a,b), max(a,b))] = c
cc = set()
i = 0
imkr = set()
while True:
    cc.add(i)
    for vv in g[i]:
        if vv not in cc:
            G[i].append(vv)
            imkr.add(vv)
    if len(imkr) == 0:
        break
    i = imkr.pop()
 
S = []
F = [0]*N
depth = [0]*N
depthh = [0]*N
vn = [[] for _ in range(N)]
sn = [[] for _ in range(N)]
iin = [[] for _ in range(N)]
aii = []
w2i = [0]*(2*N)

ii = 0
def dfs(bb, v, d, dd, cc, dpd):
    global ii
    F[v] = len(S)
    depth[v] = d
    depthh[v] = dd
    S.append(v)
    vn[cc].append(1)
    sn[cc].append(dpd)
    iin[cc].append(v)
    aii.append(v)
    w2i[v] = ii
    ii += 1
    for w in G[v]:
        nvn = cdd["{}-{}".format(min(v,w), max(v,w))]
        dpd = dp["{}-{}".format(min(v,w), max(v,w))]
        dfs(v, w, d+1, dd+dpd, nvn, dpd)
        S.append(v)
        vn[nvn].append(-1)
        sn[nvn].append(-dpd)
        iin[nvn].append(-w)
        aii.append(-w)
        w2i[-w] = ii
        ii += 1

dfs(None, 0, 0, 0, 0,0)
#print(S)
#print(vn)
#print(sn)
#print(iin)
#print(aii)
#print(w2i)
from itertools import accumulate
mmn = []
lnc = []
for vvv in vn:
    lnc.append(len(vvv))
    mmn.append(list(accumulate(vvv)))
msn = []
for vvv in sn:
    msn.append(list(accumulate(vvv)))
 
INF = (N, None)
 
M = 2*N
M0 = 2**(M-1).bit_length()
data = [INF]*(2*M0)
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])
 
def _query(a, b):
    yield INF
    a += M0; b += M0
    while a < b:
        if b & 1:
            b -= 1
            yield data[b-1]
        if a & 1:
            yield data[a-1]
            a += 1
        a >>= 1; b >>= 1
 
def query(u, v):
    fu = F[u]; fv = F[v]
    if fu > fv:
        fu, fv = fv, fu
    return S[min(_query(fu, fv+1))[1]]

def b_s(ll, mm, ms, ind, lw, hw, target_i, lncc):
    if w2i[ll[ind]] <= target_i:
        if ind+1 >= len(ll):
            return 0, 0
        if target_i < w2i[ll[ind+1]]:
            return (mm[ind], ms[ind])
        return b_s(ll, mm, ms, (ind+1 + hw)//2, ind+1, hw, target_i, lncc)
    elif w2i[ll[ind]] > target_i:
        return b_s(ll, mm, ms, (ind + lw)//2, lw, ind-1, target_i, lncc)
    return 0, 0

def iro(u, v, cc, x, y):
    if w2i[u] < w2i[iin[x][0]]:
        u_n, u_d = 0, 0
    else:
        u_n, u_d = b_s(iin[x], mmn[x], msn[x], (lnc[x]-1)//2, 0, lnc[x]-1, w2i[u], lnc[x]-1)
    if w2i[v] < w2i[iin[x][0]]:
        v_n, v_d = 0, 0
    else:
        v_n, v_d = b_s(iin[x], mmn[x], msn[x], (lnc[x]-1)//2, 0, lnc[x]-1, w2i[v], lnc[x]-1)
    if w2i[cc] < w2i[iin[x][0]]:
        c_n, c_d = 0, 0
    else:
        c_n, c_d = b_s(iin[x], mmn[x], msn[x], (lnc[x]-1)//2, 0, lnc[x]-1, w2i[cc], lnc[x]-1)
    return (u_n + v_n - 2 * (c_n)) * y - (u_d + v_d - 2 * (c_d))

 
 
#x = 2
#u_n, u_d = b_s(iin[x], mmn[x], msn[x], (lnc[x]-1)//2, 0, lnc[x]-1, w2i[2], lnc[x]-1)
#print(u_n, u_d)
#sys.exit()
for q in range(Q):
    x, y, u, v = map(int, readline().split())
    u, v = u-1, v-1
    cc = query(u, v)
    diff = 0
    if lnc[x] == 0:
        diff = 0
    else:
        diff = iro(u, v, cc, x, y)
#    print("query, col : {} v_ind : {}".format(x, v), b_s(iin[x], mmn[x], msn[x], (lnc[x]-1)//2, 0, lnc[x]-1, w2i[v], lnc[x]-1))
    print(depthh[u] + depthh[v] - 2*depthh[cc] + diff)

Submission status: Time Limit Exceeded

Solution code:
import sys
from collections import defaultdict

sys.setrecursionlimit(10 ** 5 + 5)


def solve(n, links, queries):
    def _query(a, b, data, m0, INF):
        yield INF
        a += m0
        b += m0
        while a < b:
            if b & 1:
                b -= 1
                yield data[b - 1]
            if a & 1:
                yield data[a - 1]
                a += 1
            a >>= 1
            b >>= 1

    def query(u, v):
        fu = first_appear[u]
        fv = first_appear[v]
        if fu > fv:
            fu, fv = fv, fu
        return euler_tour[min(_query(fu, fv + 1, data, m0, INF))[1]]

    def dfs(v, p, dep):
        first_appear[v] = len(euler_tour)
        depth[v] = dep
        euler_tour.append(v)
        for u in links[v]:
            if u == p:
                continue
            dfs(u, v, dep + 1)
            euler_tour.append(v)

    def dfs2(v, p, tmp_dists, total_dist):
        for x, arr in v_queries[v].items():
            arr[0] = total_dist - tmp_dists[x][0]
            arr[1] = tmp_dists[x][1]
        for u, (uc, ud) in links[v].items():
            if u == p:
                continue
            tmp_dists[uc][0] += ud
            tmp_dists[uc][1] += 1
            dfs2(u, v, tmp_dists, total_dist + ud)
            tmp_dists[uc][0] -= ud
            tmp_dists[uc][1] -= 1

    # 存在しない範囲は深さが他よりも大きくなるようにする
    INF = (n, None)

    # Euler Tour の構築
    euler_tour = []
    first_appear = [0] * n
    depth = [0] * n

    dfs(0, -1, 0)
    # print(euler_tour)
    # print(first_appear)
    # print(depth)

    # LCAを計算するクエリの前計算
    m = 2 * n
    m0 = 2 ** (m - 1).bit_length()
    data = [INF] * (2 * m0)
    for i, v in enumerate(euler_tour):
        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])

    # print(data)

    v_queries = [{} for _ in range(n)]
    lca = []
    for i, (x, y, u, v) in enumerate(queries):
        w = query(u, v)
        lca.append(w)
        v_queries[u][x] = [0, 0]
        v_queries[v][x] = [0, 0]
        if w != 0:
            v_queries[w][x] = [0, 0]

    tmp_dists = defaultdict(lambda: [0, 0])
    dfs2(0, -1, tmp_dists, 0)

    ans = []
    for w, (x, y, u, v) in zip(lca, queries):
        qu = v_queries[u][x]
        qv = v_queries[v][x]
        du = qu[0] + qu[1] * y
        dv = qv[0] + qv[1] * y
        if w == 0:
            ans.append(du + dv)
            continue
        qw = v_queries[w][x]
        dw = qw[0] + qw[1] * y
        ans.append(du + dv - 2 * dw)

    return ans


n, q = list(map(int, input().split()))
links = [{} for _ in range(n)]
lines = sys.stdin.readlines()
for line in lines[:n - 1]:
    a, b, c, d = list(map(int, line.split()))
    a -= 1
    b -= 1
    links[a][b] = (c, d)
    links[b][a] = (c, d)
queries = []
for line in lines[n - 1:]:
    x, y, u, v = map(int, line.split())
    u -= 1
    v -= 1
    queries.append((x, y, u, v))

ans = solve(n, links, queries)

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