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
from collections import defaultdict
sys.setrecursionlimit(10**7)
readline = sys.stdin.readline
 
N, Q = map(int, readline().split())
G = [[] for _ in range(N)]
dp = {}

def init():
    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

init()
S = [0]*(2*N)
F = [0]*N
depth = [0]*N
depthh = [0]*N
mmn = [[0] for _ in range(N)]
msn = [[0] for _ in range(N)]
iin = [[] for _ in range(N)]
w2i = [0]*(2*N)
ii = -1
def dfs(bb, v, d, dd, cc, dpd):
    global ii
    ii += 1
    F[v] = ii
    depth[v] = d
    depthh[v] = dd
    S[ii] = v
    mmn[cc].append(mmn[cc][-1]+1)
    msn[cc].append(msn[cc][-1]+dpd)
    iin[cc].append(v)
    w2i[v] = ii
    for w in G[v]:
        if w == bb:
            continue
        cc, dpd = dp[(min(v,w), max(v,w))]
        dfs(v, w, d+1, dd+dpd, cc, dpd)
#        bb, v, d, dd = v, w, d+1, dd+dpd
        ii += 1
        S[ii] = v
        mmn[cc].append(mmn[cc][-1]-1)
        msn[cc].append(msn[cc][-1]-dpd)
        iin[cc].append(-w)
        w2i[-w] = ii


dfs(None, 0, 0, 0, 0,0)
lnc = [len(x)-1 for x in mmn]
 
INF = (N, None)
M = 2*N
M0 = 2**(M-1).bit_length()
data = [INF]*(2*M0)

def mk_data():
    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])

mk_data()
 
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+1], ms[ind+1])
            ind, lw = (ind+1 + hw)//2, ind+1
            continue
        ind, hw = (ind-1 + lw)//2, ind-1

def process():
    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:
            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)
            diff = (u_n + v_n - 2 * (c_n)) * y - (u_d + v_d - 2 * (c_d))
        print(depthh[u] + depthh[v] - 2*depthh[cc] + diff)

if __name__ == '__main__':
    process()

Submission status: Time Limit Exceeded

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

def init():
    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

init()
S = [0]*(2*N)
F = [0]*N
depth = [0]*N
depthh = [0]*N
mmn = [[0] for _ in range(N)]
msn = [[0] for _ in range(N)]
iin = [[] for _ in range(N)]
w2i = [0]*(2*N)
ii = -1
def dfs(bb, v, d, dd, cc, dpd):
    global ii
    ii += 1
    F[v] = ii
    depth[v] = d
    depthh[v] = dd
    S[ii] = v
    mmn[cc].append(mmn[cc][-1]+1)
    msn[cc].append(msn[cc][-1]+dpd)
    iin[cc].append(v)
    w2i[v] = ii
    for w in G[v]:
        if w == bb:
            continue
        cc, dpd = dp[(min(v,w), max(v,w))]
        dfs(v, w, d+1, dd+dpd, cc, dpd)
#        bb, v, d, dd = v, w, d+1, dd+dpd
        ii += 1
        S[ii] = v
        mmn[cc].append(mmn[cc][-1]-1)
        msn[cc].append(msn[cc][-1]-dpd)
        iin[cc].append(-w)
        w2i[-w] = ii


dfs(None, 0, 0, 0, 0,0)
lnc = [len(x)-1 for x in mmn]
 
INF = (N, None)
M = 2*N
M0 = 2**(M-1).bit_length()
data = [INF]*(2*M0)

def mk_data():
    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])

mk_data()
 
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+1], ms[ind+1])
            ind, lw = (ind+1 + hw)//2, ind+1
            continue
        ind, hw = (ind-1 + lw)//2, ind-1

def process():
    for q in range(Q):
        x, y, u, v = map(int, readline().split())
        u, v = u-1, v-1
        cc = query(u, v)
        if lnc[x] == 0:
            diff = 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)
            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)
            diff = (u_n + v_n - 2 * (c_n)) * y - (u_d + v_d - 2 * (c_d))
        print(depthh[u] + depthh[v] - 2*depthh[cc] + diff)

if __name__ == '__main__':
    process()

Submission status: Time Limit Exceeded

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

def init():
    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

init()
S = [0]*(2*N)
F = [0]*N
depth = [0]*N
depthh = [0]*N
mmn = [[0] for _ in range(N)]
msn = [[0] for _ in range(N)]
iin = [[] for _ in range(N)]
w2i = [0]*(2*N)
def dfs_l():
    def dfs(bb, v, d, dd, cc, dpd):
        dfs.ii += 1
        F[v] = dfs.ii
        depth[v] = d
        depthh[v] = dd
        S[dfs.ii] = v
        mmn[cc].append(mmn[cc][-1]+1)
        msn[cc].append(msn[cc][-1]+dpd)
        iin[cc].append(v)
        w2i[v] = dfs.ii
        for w in G[v]:
            if w == bb:
                continue
            cc, dpd = dp[(min(v,w), max(v,w))]
            dfs(v, w, d+1, dd+dpd, cc, dpd)
    #        bb, v, d, dd = v, w, d+1, dd+dpd
            dfs.ii += 1
            S[dfs.ii] = v
            mmn[cc].append(mmn[cc][-1]-1)
            msn[cc].append(msn[cc][-1]-dpd)
            iin[cc].append(-w)
            w2i[-w] = dfs.ii
    dfs.ii = -1
    dfs(None, 0, 0, 0, 0,0)

dfs_l()
lnc = [len(x)-1 for x in mmn]
 
INF = (N, None)
M = 2*N
M0 = 2**(M-1).bit_length()
data = [INF]*(2*M0)

def mk_data():
    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])

mk_data()
 
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
    for _ in range(N):
        if w2i[ll[ind]] <= target_i:
            if target_i < w2i[ll[ind+1]]:
                return (mm[ind+1], ms[ind+1])
            ind, lw = (ind+1 + hw)//2, ind+1
            continue
        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))

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

process()

Submission status: Time Limit Exceeded

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

def init():
    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

init()
S = [0]*(2*N)
F = [0]*N
depth = [0]*N
depthh = [0]*N
mmn = [[0] for _ in range(N)]
msn = [[0] for _ in range(N)]
iin = [[] for _ in range(N)]
w2i = [0]*(2*N)
ii = -1
def dfs(bb, v, d, dd, cc, dpd):
    global ii
    ii += 1
    F[v] = ii
    depth[v] = d
    depthh[v] = dd
    S[ii] = v
    mmn[cc].append(mmn[cc][-1]+1)
    msn[cc].append(msn[cc][-1]+dpd)
    iin[cc].append(v)
    w2i[v] = ii
    for w in G[v]:
        if w == bb:
            continue
        cc, dpd = dp[(min(v,w), max(v,w))]
        dfs(v, w, d+1, dd+dpd, cc, dpd)
#        bb, v, d, dd = v, w, d+1, dd+dpd
        ii += 1
        S[ii] = v
        mmn[cc].append(mmn[cc][-1]-1)
        msn[cc].append(msn[cc][-1]-dpd)
        iin[cc].append(-w)
        w2i[-w] = ii


dfs(None, 0, 0, 0, 0,0)
lnc = [len(x)-1 for x in mmn]
 
INF = (N, None)
M = 2*N
M0 = 2**(M-1).bit_length()
data = [INF]*(2*M0)

def mk_data():
    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])

mk_data()
 
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
    for _ in range(N):
        if w2i[ll[ind]] <= target_i:
            if target_i < w2i[ll[ind+1]]:
                return (mm[ind+1], ms[ind+1])
            ind, lw = (ind+1 + hw)//2, ind+1
            continue
        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))

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

process()

Submission status: Time Limit Exceeded

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

N, Q = map(int, readline().split())
INF = (N, None)
M = 2*N
M0 = 2**(M-1).bit_length()


class f2:
    def __init__(self):
        self.ii = -1
        self.G = [[] for _ in range(N)]
        self.dp = {}

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

        self.S, self.F, self.w2i = [0]*(2*N), [0]*N, [0]*(2*N)
        self.depth, self.depthh = [0]*N, [0]*N
        self.mmn, self.msn, self.iin = [[0] for _ in range(N)], [[0] for _ in range(N)], [[] for _ in range(N)]

        self.dfs(None, 0, 0, 0, 0,0)
        self.lnc = [len(x)-1 for x in self.mmn]
         
        self.data = [INF]*(2*M0)
        for i, v in enumerate(self.S):
            self.data[M0-1+i] = (self.depth[v], i)
        for i in range(M0-2, -1, -1):
            self.data[i] = min(self.data[2*i+1], self.data[2*i+2])
         

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

    def dfs(self, bb, v, d, dd, cc, dpd):
        self.ii += 1
        self.F[v] = self.ii
        self.depth[v] = d
        self.depthh[v] = dd
        self.S[self.ii] = v
        self.mmn[cc].append(self.mmn[cc][-1]+1)
        self.msn[cc].append(self.msn[cc][-1]+dpd)
        self.iin[cc].append(v)
        self.w2i[v] = self.ii
        for w in self.G[v]:
            if w == bb:
                continue
            cc, dpd = self.dp[(min(v,w), max(v,w))]
            self.dfs(v, w, d+1, dd+dpd, cc, dpd)
    #        bb, v, d, dd = v, w, d+1, dd+dpd
            self.ii += 1
            self.S[self.ii] = v
            self.mmn[cc].append(self.mmn[cc][-1]-1)
            self.msn[cc].append(self.msn[cc][-1]-dpd)
            self.iin[cc].append(-w)
            self.w2i[-w] = self.ii

    def b_s(self, ll, mm, ms, ind, lw, hw, target_i, lncc):
        w2i = self.w2i
        if target_i < w2i[ll[0]] or 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+1], ms[ind+1])
                ind, lw = (ind+1 + hw)//2, ind+1
                continue
            ind, hw = (ind-1 + lw)//2, ind-1

    def iro(self, u, v, cc, x, y):
        iin, mmn, msn, lnc, w2i = self.iin, self.mmn, self.msn, self.lnc, self.w2i
        u_n, u_d = self.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 = self.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 = self.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))

    def _query(self, a, b):
        yield INF
        a += M0; b += M0
        while a < b:
            if b & 1:
                b -= 1
                yield self.data[b-1]
            if a & 1:
                yield self.data[a-1]
                a += 1
            a >>= 1; b >>= 1
     
    def query(self, u, v):
        fu = self.F[u]; fv = self.F[v]
        if fu > fv:
            fu, fv = fv, fu
        return self.S[min(self._query(fu, fv+1))[1]]


if __name__ == '__main__':
    f2()

Submission status: Time Limit Exceeded

Solution code:
import sys
from collections import defaultdict
sys.setrecursionlimit(10**7)
readline = sys.stdin.readline
 
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[(min(a,b), max(a,b))] = c, d
 
S = [0]*(2*N)
F = [0]*N
depth = [0]*N
depthh = [0]*N
mmn = [[0] for _ in range(N)]
msn = [[0] for _ in range(N)]
iin = [[] for _ in range(N)]
w2i = [0]*(2*N)
ii = -1
def dfs(bb, v, d, dd, cc, dpd):
    global ii
    ii += 1
    F[v] = ii
    depth[v] = d
    depthh[v] = dd
    S[ii] = v
    mmn[cc].append(mmn[cc][-1]+1)
    msn[cc].append(msn[cc][-1]+dpd)
    iin[cc].append(v)
    w2i[v] = ii
    for w in G[v]:
        if w == bb:
            continue
        cc, dpd = dp[(min(v,w), max(v,w))]
        dfs(v, w, d+1, dd+dpd, cc, dpd)
#        bb, v, d, dd = v, w, d+1, dd+dpd
        ii += 1
        S[ii] = v
        mmn[cc].append(mmn[cc][-1]-1)
        msn[cc].append(msn[cc][-1]-dpd)
        iin[cc].append(-w)
        w2i[-w] = ii


dfs(None, 0, 0, 0, 0,0)
lnc = [len(x)-1 for x in mmn]
 
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
    for _ in range(N):
        if w2i[ll[ind]] <= target_i:
            if target_i < w2i[ll[ind+1]]:
                return (mm[ind+1], ms[ind+1])
            ind, lw = (ind+1 + hw)//2, ind+1
            continue
        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, readline().split())
    u, v = u-1, v-1
    cc = query(u, v)
    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
sys.setrecursionlimit(10**7)
readline = sys.stdin.readline
 
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[(min(a,b), max(a,b))] = c, d
 
S = [0]*(2*N)
F = [0]*N
depth = [0]*N
depthh = [0]*N
mmn = [[0] for _ in range(N)]
msn = [[0] for _ in range(N)]
iin = [[] for _ in range(N)]
w2i = [0]*(2*N)
ii = -1
def dfs(bb, v, d, dd, cc, dpd):
    global ii
    ii += 1
    F[v] = ii
    depth[v] = d
    depthh[v] = dd
    S[ii] = v
    mmn[cc].append(mmn[cc][-1]+1)
    msn[cc].append(msn[cc][-1]+dpd)
    iin[cc].append(v)
    w2i[v] = ii
    for w in G[v]:
        if w == bb:
            continue
        cc, dpd = dp[(min(v,w), max(v,w))]
        dfs(v, w, d+1, dd+dpd, cc, dpd)
#        bb, v, d, dd = v, w, d+1, dd+dpd
        ii += 1
        S[ii] = v
        mmn[cc].append(mmn[cc][-1]-1)
        msn[cc].append(msn[cc][-1]-dpd)
        iin[cc].append(-w)
        w2i[-w] = ii


dfs(None, 0, 0, 0, 0,0)
lnc = [len(x)-1 for x in mmn]
 
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+1], ms[ind+1])
            ind, lw = (ind+1 + hw)//2, ind+1
            continue
        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, readline().split())
    u, v = u-1, v-1
    cc = query(u, v)
    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
sys.setrecursionlimit(10**7)
readline = sys.stdin.readline
 
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[(min(a,b), max(a,b))] = c, d
 
S = []
F = [0]*N
depth = [0]*N
depthh = [0]*N
mmn = [[0] for _ in range(N)]
msn = [[0] 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)
    mmn[cc].append(mmn[cc][-1]+1)
    msn[cc].append(msn[cc][-1]+dpd)
    iin[cc].append(v)
    w2i[v] = ii
    ii += 1
    for w in G[v]:
        if w == bb:
            continue
        cc, dpd = dp[(min(v,w), max(v,w))]
        dfs(v, w, d+1, dd+dpd, cc, dpd)
#        bb, v, d, dd = v, w, d+1, dd+dpd
        S.append(v)
        mmn[cc].append(mmn[cc][-1]-1)
        msn[cc].append(msn[cc][-1]-dpd)
        iin[cc].append(-w)
        w2i[-w] = ii
        ii += 1



dfs(None, 0, 0, 0, 0,0)
lnc = [len(x)-1 for x in mmn]
 
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+1], ms[ind+1])
            ind, lw = (ind+1 + hw)//2, ind+1
            continue
        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, readline().split())
    u, v = u-1, v-1
    cc = query(u, v)
    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
sys.setrecursionlimit(10**7)
readline = sys.stdin.readline
 
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
mmn = [[0] for _ in range(N)]
msn = [[0] 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)
    mmn[cc].append(mmn[cc][-1]+1)
    msn[cc].append(msn[cc][-1]+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)
        mmn[nvn].append(mmn[nvn][-1]-1)
        msn[nvn].append(msn[nvn][-1]-dpd)
        iin[nvn].append(-w)
        w2i[-w] = ii
        ii += 1


dfs(None, 0, 0, 0, 0,0)
lnc = [len(x)-1 for x in mmn]
 
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+1], ms[ind+1])
            ind, lw = (ind+1 + hw)//2, ind+1
            continue
        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, readline().split())
    u, v = u-1, v-1
    cc = query(u, v)
    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)
 
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
mmn = [[0] for _ in range(N)]
msn = [[0] 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)
    mmn[cc].append(mmn[cc][-1]+1)
    msn[cc].append(msn[cc][-1]+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)
        mmn[nvn].append(mmn[nvn][-1]-1)
        msn[nvn].append(msn[nvn][-1]-dpd)
        iin[nvn].append(-w)
        w2i[-w] = ii
        ii += 1


dfs(None, 0, 0, 0, 0,0)
lnc = [len(x)-1 for x in mmn]
 
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+1], ms[ind+1])
            ind, lw = (ind+1 + hw)//2, ind+1
            continue
        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)
    if lnc[x] == 0:
        diff = 0
    else:
        diff = iro(u, v, cc, x, y)
    print(depthh[u] + depthh[v] - 2*depthh[cc] + diff)