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\n\ninput = sys.stdin.readline\nsys.setrecursionlimit(100000)\n\n\ndef read_values():\n    return list(map(int, input().split()))\n\n\ndef read_index():\n    return [int(x) - 1 for x in input().split()]\n\n\ndef read_list():\n    return list(read_values())\n\n\ndef read_lists(N):\n    return [read_list() for n in range(N)]\n\n\nclass V:\n    def __init__(self, f, v=None):\n        self.f = f\n        self.v = v\n\n    def __str__(self):\n        return str(self.v)\n\n    def ud(self, n):\n        if n is None:\n            return\n\n        if self.v is None:\n            self.v = n\n            return\n        self.v = self.f(self.v, n)\n\n\nclass LCA:\n    def __init__(self, N, L):\n        self.L = L\n        self.INF = (N, None)\n        self.M0 = 2 ** (2 * N - 1).bit_length()\n        self.data = [self.INF] * (2 * self.M0)\n        self.D = [0] * N\n        self.F = [0] * N\n        self.S = []\n        self.dist = [0] * N\n\n        self.dfs1(0, 0, -1)\n        for i, v in enumerate(self.S):\n            self.data[self.M0 - 1 + i] = (self.D[v], i)\n        for i in range(self.M0 - 2, -1, -1):\n            self.data[i] = min(self.data[2 * i + 1], self.data[2 * i + 2])\n\n    def dfs1(self, v, d, p, pd=0):\n        self.F[v] = len(self.S)\n        self.D[v] = d\n        self.S.append(v)\n        self.dist[v] = pd\n        for w, c, dis in self.L[v]:\n            if w == p:\n                continue\n            self.dfs1(w, d + 1, v, pd + dis)\n            self.S.append(v)\n\n    def _query(self, a, b):\n        yield self.INF\n        a += self.M0\n        b += self.M0\n        while a < b:\n            if b & 1:\n                b -= 1\n                yield self.data[b - 1]\n            if a & 1:\n                yield self.data[a - 1]\n                a += 1\n            a >>= 1\n            b >>= 1\n\n    def query(self, u, v):\n        fu = self.F[u]\n        fv = self.F[v]\n        if fu > fv:\n            fu, fv = fv, fu\n        return self.S[min(self._query(fu, fv + 1))[1]]\n\n    def dist(self, v):\n        return self.dist[v]\n\n\ndef dfs2(L, v, p, QS, ans, CC, CD):\n    for q, x, y, f in QS[v]:\n        ans[q] += (y * CC[x] - CD[x]) * f\n\n    for w, c, dis in L[v]:\n        if w == p:\n            continue\n        CC[c] += 1\n        CD[c] += dis\n        dfs2(L, w, v, QS, ans, CC, CD)\n        CC[c] -= 1\n        CD[c] -= dis\n\n\ndef main():\n    N, Q = read_values()\n    L = [[] for _ in range(N)]\n    for _ in range(N - 1):\n        a, b, c, d = read_values()\n        a -= 1\n        b -= 1\n        c -= 1\n        L[a].append((b, c, d))\n        L[b].append((a, c, d))\n\n    g = LCA(N, L)\n\n    QS = [[] for _ in range(N)]\n    ans = [0] * Q\n    for q in range(Q):\n        x, y, u, v = read_values()\n        x -= 1\n        u -= 1\n        v -= 1\n        w = g.query(u, v)\n        ans[q] = g.dist[u] + g.dist[v] - 2 * g.dist[w]\n        QS[u].append((q, x, y, 1))\n        QS[v].append((q, x, y, 1))\n        QS[w].append((q, x, y, -2))\n\n    CC = [0] * N\n    CD = [0] * N\n    dfs2(L, 0, -1, QS, ans, CC, CD)\n\n    print(("\\n".join(map(str, ans))))\n\n\ndef __starting_point():\n    main()\n\n__starting_point()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 22159