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\nfrom collections import defaultdict\n\nsys.setrecursionlimit(10 ** 5 + 5)\n\n\ndef solve(n, links, queries):\n    def _query(a, b, data, m0, INF):\n        yield INF\n        a += m0\n        b += m0\n        while a < b:\n            if b & 1:\n                b -= 1\n                yield data[b - 1]\n            if a & 1:\n                yield data[a - 1]\n                a += 1\n            a >>= 1\n            b >>= 1\n\n    def query(u, v):\n        fu = first_appear[u]\n        fv = first_appear[v]\n        if fu > fv:\n            fu, fv = fv, fu\n        return euler_tour[min(_query(fu, fv + 1, data, m0, INF))[1]]\n\n    def dfs(v, p, dep):\n        first_appear[v] = len(euler_tour)\n        depth[v] = dep\n        euler_tour.append(v)\n        for u, _, _ in links[v]:\n            if u == p:\n                continue\n            dfs(u, v, dep + 1)\n            euler_tour.append(v)\n\n    def dfs2(v, p, tmp_dists, total_dist):\n        for x, arr in list(v_queries[v].items()):\n            arr[0] = total_dist - tmp_dists[x][0]\n            arr[1] = tmp_dists[x][1]\n        for u, uc, ud in links[v]:\n            if u == p:\n                continue\n            tmp_dists[uc][0] += ud\n            tmp_dists[uc][1] += 1\n            dfs2(u, v, tmp_dists, total_dist + ud)\n            tmp_dists[uc][0] -= ud\n            tmp_dists[uc][1] -= 1\n\n    # 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\n    INF = (n, None)\n\n    # Euler Tour の構築\n    euler_tour = []\n    first_appear = [0] * n\n    depth = [0] * n\n\n    dfs(0, -1, 0)\n    # print(euler_tour)\n    # print(first_appear)\n    # print(depth)\n\n    # LCAを計算するクエリの前計算\n    m = 2 * n\n    m0 = 2 ** (m - 1).bit_length()\n    data = [INF] * (2 * m0)\n    for i, v in enumerate(euler_tour):\n        data[m0 - 1 + i] = (depth[v], i)\n    for i in range(m0 - 2, -1, -1):\n        data[i] = min(data[2 * i + 1], data[2 * i + 2])\n\n    # print(data)\n\n    v_queries = [{} for _ in range(n)]\n    lca = []\n    for i, (x, y, u, v) in enumerate(queries):\n        w = query(u, v)\n        lca.append(w)\n        v_queries[u][x] = [0, 0]\n        v_queries[v][x] = [0, 0]\n        if w != 0:\n            v_queries[w][x] = [0, 0]\n\n    tmp_dists = defaultdict(lambda: [0, 0])\n    dfs2(0, -1, tmp_dists, 0)\n\n    ans = []\n    for w, (x, y, u, v) in zip(lca, queries):\n        qu = v_queries[u][x]\n        qv = v_queries[v][x]\n        du = qu[0] + qu[1] * y\n        dv = qv[0] + qv[1] * y\n        if w == 0:\n            ans.append(du + dv)\n            continue\n        qw = v_queries[w][x]\n        dw = qw[0] + qw[1] * y\n        ans.append(du + dv - 2 * dw)\n\n    return ans\n\n\nn, q = list(map(int, input().split()))\nlinks = [set() for _ in range(n)]\nlines = sys.stdin.readlines()\nfor line in lines[:n - 1]:\n    a, b, c, d = list(map(int, line.split()))\n    a -= 1\n    b -= 1\n    links[a].add((b, c, d))\n    links[b].add((a, c, d))\nqueries = []\nfor line in lines[n - 1:]:\n    x, y, u, v = list(map(int, line.split()))\n    u -= 1\n    v -= 1\n    queries.append((x, y, u, v))\n\nans = solve(n, links, queries)\n\nprint(('\\n'.join(map(str, ans))))\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 17098