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-----
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

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.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'import sys\nsys.setrecursionlimit(10**6)\ninput = sys.stdin.readline\n \nINF = 10**6\n \nclass RMQ:\n    def __init__(self, a):\n        self.n = len(a)\n        self.size = 2**(self.n - 1).bit_length()\n        self.data = [(INF, INF) for _ in range(2*self.size-1)]\n        self.initialize(a)\n \n    # Initialize data\n    def initialize(self, a):\n        for i in range(self.n):\n            self.data[self.size + i - 1] = a[i][:]\n        for i in range(self.size-2, -1, -1):\n            self.data[i] = min(self.data[i*2 + 1], self.data[i*2 + 2])[:]\n    \n    # Update ak as x\n    def update(self, k, x):\n        k += self.size - 1\n        self.data[k] = x\n        while k > 0:\n            k = (k - 1) // 2\n            self.data[k] = min(self.data[2*k+1], self.data[2*k+2])[:]\n    \n    # Min value in [l, r)\n    def query(self, l, r):\n        L = l + self.size; R = r + self.size\n        s = (INF, INF)\n        while L < R:\n            if R & 1:\n                R -= 1\n                s = min(s, self.data[R-1])[:]\n            if L & 1:\n                s = min(s, self.data[L-1])[:]\n                L += 1\n            L >>= 1; R >>= 1\n        return s\n \nclass LCA:\n    def __init__(self, edge, root):\n        self.itr = 0\n        self.edge = edge[:]\n        self.path = [0] * (2*n-1)\n        self.depth = [0] * (2*n-1)\n        self.color = [0] * (2*n-1)\n        self.weight = [0] * (2*n-1)\n        self.index = [0] * n\n        self.euler_tour(-1, root, 0, 0, 0, 0)\n        dat = list(zip(self.depth, self.path))\n        self.rmq = RMQ(dat)\n    \n    # Lowest ancestor of u, v\n    def get_lca(self, u, v):\n        l, r = self.index[u], self.index[v]\n        if l > r:\n            l, r = r, l\n        return self.rmq.query(l, r+1)[1]\n    \n    def euler_tour(self, prev, v, d, k, c, w):\n        self.index[v] = k\n        self.path[self.itr] = v\n        self.depth[self.itr] = d\n        self.color[self.itr] = c\n        self.weight[self.itr] = w\n        self.itr += 1\n        k += 1\n        for dest, c, w in self.edge[v]:\n            if prev == dest:\n                continue\n            k = self.euler_tour(v, dest, d + 1, k, c, w)\n            self.path[self.itr] = v\n            self.depth[self.itr] = d\n            self.color[self.itr] = -c\n            self.weight[self.itr] = -w\n            self.itr += 1\n            k += 1\n        return k\n        \nn, q = [int(item) for item in input().split()] \nedge = [[] for _ in range(n)]\n \nfor _ in range(n-1):\n    u, v, c, w = [int(item) for item in input().split()]\n    u -= 1; v -= 1\n    edge[u].append((v, c, w))\n    edge[v].append((u, c, w))\n \nlca = LCA(edge, 0)\nmemo = [dict() for _ in range(n)]\nlca_memo = dict()\n \nquery = []\nfor _ in range(q):\n    x, y, u, v = [int(item) for item in input().split()]\n    u -= 1; v -= 1\n    if u > v:\n        u, v = v, u\n    if (u, v) in lca_memo:\n        ca = lca_memo[(u, v)]\n    else:\n        ca = lca.get_lca(u, v)\n        lca_memo[(u, v)] = ca\n    memo[u][x] = None\n    memo[v][x] = None\n    memo[ca][x] = None\n    query.append((x, y, ca, u, v))\n \ncolors = [0] * n\nc_depth = [0] * n\ndepth = 0\nfor p, c, w in zip(lca.path[1:], lca.color[1:], lca.weight[1:]):\n    color = abs(c)\n    if c < 0:\n        colors[color] -= 1\n    else:\n        colors[color] += 1\n    c_depth[color] += w\n    depth += w\n \n    for key in memo[p].keys():\n        if memo[p][key] != None:\n            break\n        memo[p][key] = (colors[key], c_depth[key])\n    memo[p][0] = depth \n \nans = []\nfor x, y, ca, u, v in query:\n    # Calc basic distance\n    val = memo[u][0] + memo[v][0] - memo[ca][0] * 2\n    # Append color diff\n    val += (memo[v][x][0] + memo[u][x][0] - memo[ca][x][0] * 2) * y \n    val -= (memo[v][x][1] + memo[u][x][1] - memo[ca][x][1] * 2)\n    ans.append(val)\nprint("\\n".join(map(str,ans)))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 22859