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**7)\n\ndef main0(n,g,xyuv):\n  # LCAを求める。自作する。\n  # 各頂点の深さ。根は深さ0\n  depth=[0]*n\n  tour=[]\n  hatsu=[0]*n\n  dist=[0]*n\n  tmp=0\n  def et(p,v,tour,tmp,pc,pd):\n    hatsu[v]=len(tour)-1\n    for nv,c,d in g[v]:\n      if nv==p:continue\n      depth[nv]=depth[v]+1\n      tmp+=d\n      dist[nv]=tmp\n      tour.append((nv,c,d))\n      tour=et(v,nv,tour,tmp,c,d)\n      tmp-=d\n      tour.append((v,c,-d))\n    return tour\n  tour.append((0,0,0))\n  tour=et(-1,0,tour,0,0,0)\n  class SegmentTree():\n    def __init__(self,size,f=lambda x,y:x+y,default=0):\n      self.size=pow(2,(size-1).bit_length())\n      self.f=f\n      self.default=default\n      self.data=[default]*(self.size*2)\n    def update(self,i,x):\n      i+=self.size\n      self.data[i]=x\n      while i:\n        i>>=1\n        self.data[i]=self.f(self.data[i*2],self.data[i*2+1])\n    # 区間[l,r)へのクエリ\n    def query(self,l,r):\n      l,r=l+self.size,r+self.size\n      lret,rret=self.default,self.default\n      while l<r:\n        if l&1:\n          lret=self.f(self.data[l],lret)\n          l+=1\n        if r&1:\n          r-=1\n          rret=self.f(self.data[r],rret)\n        l>>=1\n        r>>=1\n      return self.f(lret,rret)\n\n  def func(x,y):\n    if x[0]<y[0]:return x\n    return y\n  st=SegmentTree(len(tour),func,(n+1,0))\n  for i,x in enumerate(tour):\n    v=x[0]\n    st.update(i,(depth[v],v))\n  def lca(u,v):\n    x,y=hatsu[u],hatsu[v]\n    if x<y:\n      y+=1\n    else:\n      x,y=y,x\n      y+=1\n    return st.query(x,y)[1]\n  dc={}\n  dcary={}\n  for i,(v,c,d) in enumerate(tour):\n    if c in dc:\n      ci=1 if d>0 else -1\n      dc[c].append((dc[c][-1][0]+ci,dc[c][-1][1]+d))\n      dcary[c].append(i)\n    else:\n      dc[c]=[(0,0),(1,d)]\n      dcary[c]=[0,i]\n  ret=[]\n  from bisect import bisect_right as bl\n  for x,y,u,v in xyuv:\n    u,v=u-1,v-1\n    w=lca(u,v)\n    uvlen=dist[u]+dist[v]-dist[w]*2\n    if x not in dc:\n      ret.append(uvlen)\n      continue\n    widx=bl(dcary[x],hatsu[w])-1\n    wnum,wsum=dc[x][widx]\n    uidx=bl(dcary[x],hatsu[u])-1\n    vidx=bl(dcary[x],hatsu[v])-1\n    unum,usum=dc[x][uidx]\n    vnum,vsum=dc[x][vidx]\n    uvsum=usum+vsum-wsum*2\n    uvnum=unum+vnum-wnum*2\n    #print(uvlen-uvsum+uvnum*y,uvlen,usum,vsum,wsum,uvnum,w)\n    ret.append(uvlen-uvsum+uvnum*y)\n  return ret\n\ndef __starting_point():\n  n,q=map(int,input().split())\n  abcd=[list(map(int,input().split())) for _ in range(n-1)]\n  xyuv=[list(map(int,input().split())) for _ in range(q)]\n  g=[[] for _ in range(n)]\n  for a,b,c,d in abcd:\n    a,b=a-1,b-1\n    g[a].append((b,c,d))\n    g[b].append((a,c,d))\n  ary0=main0(n,g,xyuv)\n  print(*ary0,sep='\\n')\n\n__starting_point()"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 19868