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\n\nN,Q=list(map(int,input().split()))\nEDGE=[list(map(int,input().split())) for i in range(N-1)]\nQuery=[list(map(int,input().split())) for i in range(Q)]\nmod=10**9+7\n\nEDGELIST=[dict() for i in range(N+1)]\nfor x,y,c,l in EDGE:\n    EDGELIST[x][y]=(c,l)\n    EDGELIST[y][x]=(c,l)\n    \n# LCA(オイラーツアー＋Segment tree)\n\nDEPTH=[-1]*(N+1)\nDEPTH[1]=0\n\nfrom collections import deque\nQUE = deque([1])\nQUE2 = deque()\nEULER=[]#(i,j)で,(1からツアーで辿った点の深さ,そのindex)\n\nUSED=[0]*(N+1)\nwhile QUE:\n    x=QUE.pop()\n    EULER.append((DEPTH[x],x))\n    if USED[x]==1:\n        continue\n    for to in EDGELIST[x]:\n        \n        if USED[to]==0:\n            DEPTH[to]=DEPTH[x]+1\n            QUE2.append(to)\n        else:\n            QUE.append(to)\n    QUE.extend(QUE2)\n    QUE2=deque()\n \n    USED[x]=1\n\nMINP=[1<<30]*(N+1)\nMAXP=[-1]*(N+1)\n\nfor ind,(depth,p) in enumerate(EULER):\n    MINP[p]=min(MINP[p],ind)\n    MAXP[p]=ind\n\nLEN=len(EULER)\n\nseg_el=1<<(LEN.bit_length())#Segment treeの台の要素数\nSEG=[(1<<30,0)]*(2*seg_el)#1-indexedなので、要素数2*seg_el.Segment treeの初期値で初期化\n\nfor i in range(LEN):#Dを対応する箇所へupdate\n    SEG[i+seg_el]=EULER[i]\n\nfor i in range(seg_el-1,0,-1):#親の部分もupdate\n    SEG[i]=min(SEG[i*2],SEG[i*2+1])\n\ndef update(n,x,seg_el):#A[n]をxへ更新（反映）\n    i=n+seg_el\n    SEG[i]=x\n    i>>=1#子ノードへ\n    \n    while i!=0:\n        SEG[i]=min(SEG[i*2],SEG[i*2+1])\n        i>>=1\n        \ndef getvalues(l,r):#区間[l,r)に関するminを調べる\n    L=l+seg_el\n    R=r+seg_el\n    ANS=(1<<30,0)\n\n    while L<R:\n        if L & 1:\n            ANS=min(ANS , SEG[L])\n            L+=1\n\n        if R & 1:\n            R-=1\n            ANS=min(ANS , SEG[R])\n        L>>=1\n        R>>=1\n\n    return ANS\n\ndef LCA(l,r):\n    return getvalues(min(MINP[l],MINP[r]),max(MAXP[l],MAXP[r])+1)\n\nN_q=[[] for i in range(N+1)]\nfor ind,(c,pl,x,y) in enumerate(Query):\n    N_q[x].append([ind,c,pl,1])\n    N_q[y].append([ind,c,pl,1])\n    N_q[LCA(x,y)[1]].append([ind,c,pl,0])\n\nANS=[0]*Q\n\nLENG=0\nC_LENGTH=[0]*N\nC_SUM=[0]*N\n\nfor i in range(1,len(EULER)):\n    ind=EULER[i][1]\n    c,l=EDGELIST[EULER[i-1][1]][ind]\n    if EULER[i][0]>EULER[i-1][0]:\n        LENG+=l\n        C_LENGTH[c]+=l\n        C_SUM[c]+=1\n\n        for que,c,pl,boo in N_q[ind]:\n            if boo==1:\n                ANS[que]+=LENG+C_SUM[c]*pl-C_LENGTH[c]\n\n            else:\n                ANS[que]-=(LENG+C_SUM[c]*pl-C_LENGTH[c])*2\n            \n    else:\n        LENG-=l\n        C_LENGTH[c]-=l\n        C_SUM[c]-=1\n\nfor ans in ANS:\n    print(ans)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 23239