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\ninput = sys.stdin.readline\nsys.setrecursionlimit(10**7)\nimport numpy as np\n\nN,Q = map(int,input().split())\ngraph = [[] for _ in range(N+1)]\nfor _ in range(N-1):\n    a,b,c,d = map(int,input().split())\n    graph[a].append((b,c,d))\n    graph[b].append((a,c,d))\nquery = [[int(x) for x in input().split()] for _ in range(Q)]\n\ndef euler_tour(x, tour_v, tour_d, depth = 0, parent=None):\n    tour_v.append(x)\n    tour_d.append(depth)\n    for y, c, d in graph[x]:\n        if y == parent:\n            continue\n        euler_tour(y, tour_v, tour_d, depth + 1, parent = x)\n        tour_v.append(x)\n        tour_d.append(depth)\n\ntour_v = []\ntour_d = []\neuler_tour(1, tour_v, tour_d)\ntour_d_arr = np.array(tour_d)\nv_to_i = {v:i for i,v in enumerate(tour_v)}\nv_to_d = dict(zip(tour_v, tour_d))\n\n# sparse table\n# 各インデックスから、2^i 項目分見て、一番depthの小さいインデックス\nL = len(tour_v)\nU = L.bit_length()\nsp = [np.arange(L)]\nfor i in range(1,U):\n    prev = sp[-1]\n    width = 1 << (i-1)\n    n1 = prev[:-width]\n    n2 = prev[width:]\n    sp.append(np.where(tour_d_arr[n1] < tour_d_arr[n2], n1, n2))\n\ndef LCA(x,y):\n    ix = v_to_i[x]\n    iy = v_to_i[y]\n    if ix > iy:\n        ix,iy = iy,ix\n    items = iy - ix + 1\n    L = items.bit_length() - 1\n    n1 = sp[L][ix]\n    n2 = sp[L][iy - (1 << L) + 1]\n    n = n1 if tour_d[n1] < tour_d[n2] else n2\n    return tour_v[n]\n\ntasks = [[] for _ in range(N+1)]\nfor i,(x,y,u,v) in enumerate(query):\n    tasks[u].append((i,x,y,1))\n    tasks[v].append((i,x,y,1))\n    tasks[LCA(u,v)].append((i,x,y,-2))\n\nanswer = [0] * Q\n\ndef dfs(x = 1, sums = [0] * (N+1), nums = [0] * (N+1), total = 0, parent = 0):\n    for i,c,d,coef in tasks[x]:\n        answer[i] += coef * (total - sums[c] + nums[c] * d)\n    for y,c,d in graph[x]:\n        if y == parent:\n            continue\n        sums[c] += d\n        nums[c] += 1\n        total += d\n        dfs(y, sums, nums, total, x)\n        sums[c] -= d\n        nums[c] -= 1\n        total -= d\n    return\n\ndfs()\nprint('\\n'.join(map(str,answer)))"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 6171383