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 = "from bisect import bisect_left, bisect_right\nimport sys\ninput = sys.stdin.readline\nsys.setrecursionlimit(10**9)\n\ndef solve():\n    INF = float('inf')\n\n    N, Q = list(map(int, input().split()))\n    adjL = [[] for _ in range(N)]\n    for _ in range(N-1):\n        A, B, C, D = list(map(int, input().split()))\n        A, B, C = A-1, B-1, C-1\n        adjL[A].append((B, C, D))\n        adjL[B].append((A, C, D))\n    querys = [tuple(map(int, input().split())) for _ in range(Q)]\n\n    def dfs(vNow, vPar, depth):\n        iVFirsts[vNow] = len(vs)\n        vs.append(vNow)\n        depths.append(depth)\n        for v2, clr, dist in adjL[vNow]:\n            if v2 == vPar: continue\n            iVColorss[clr].append(len(numEs))\n            numEs.append(1)\n            sumDs.append(dist)\n\n            dfs(v2, vNow, depth+1)\n\n            vs.append(vNow)\n            depths.append(depth)\n            iVColorss[clr].append(len(numEs))\n            numEs.append(-1)\n            sumDs.append(-dist)\n\n    vs = []\n    iVFirsts = [-1] * N\n    depths = []\n    numEs = [0]\n    sumDs = [0]\n    iVColorss = [[0] for _ in range(N-1)]\n\n    dfs(0, -1, 0)\n\n    dists = [0] * N\n    accD = 0\n    for i, sumD in enumerate(sumDs):\n        accD += sumD\n        if iVFirsts[vs[i]] == i:\n            dists[vs[i]] = accD\n\n    for iVColors in iVColorss:\n        for i in range(1, len(iVColors)):\n            numEs[iVColors[i]] += numEs[iVColors[i-1]]\n            sumDs[iVColors[i]] += sumDs[iVColors[i-1]]\n\n    idEle = (INF, -1)\n    def _binOpe(x, y):\n        return x if x <= y else y  # min\n    def makeSegTree(numEle):\n        numPow2 = 2 ** (numEle-1).bit_length()\n        data = [idEle] * (2*numPow2)\n        return data, numPow2\n    def setInit(As):\n        for iST, A in enumerate(As, numPow2):\n            data[iST] = A\n        for iST in reversed(list(range(1, numPow2))):\n            data[iST] = _binOpe(data[2*iST], data[2*iST+1])\n    def getValue(iSt, iEn):\n        L = iSt + numPow2\n        R = iEn + numPow2\n        ans = idEle\n        while L < R:\n            if L & 1:\n                ans = _binOpe(ans, data[L])\n                L += 1\n            if R & 1:\n                R -= 1\n                ans = _binOpe(ans, data[R])\n            L >>= 1\n            R >>= 1\n        return ans\n\n    data, numPow2 = makeSegTree(len(depths))\n    setInit([(depth, i) for i, depth in enumerate(depths)])\n\n    def getLCA(x, y):\n        L, R = iVFirsts[x], iVFirsts[y]\n        if L > R:\n            L, R = R, L\n        minV, iMinV = getValue(L, R)\n        return vs[iMinV]\n\n    anss = []\n    for clr, distNew, u, v in querys:\n        u, v = u-1, v-1\n        LCA = getLCA(u, v)\n\n        clr -= 1\n        ds = [dists[u], dists[v], dists[LCA]]\n        for i, vv in enumerate([u, v, LCA]):\n            iIV = bisect_right(iVColorss[clr], iVFirsts[vv]) - 1\n            iV = iVColorss[clr][iIV]\n            ds[i] += numEs[iV] * distNew - sumDs[iV]\n        ans = ds[0] + ds[1] - 2*ds[2]\n        anss.append(ans)\n\n    print(('\\n'.join(map(str, anss))))\n\n\nsolve()\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 15947