Problem:
Score : 600 points

Problem Statement

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 1

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 1

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.

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Collections;
using System.Collections.Specialized;
using System.Linq;
using System.Text;
using System.IO;
using System.Reflection;
using static System.Math;
using System.Numerics;
static class Program{
	const int mod=(int)1e9+7;
	static List<Tuple<int,int,int>>[] li;
	static List<Tuple<int,int>>[] li2;
	static bool[] b;
	static int[] h,ix,di,c1,c2,ans;
	static int[][] z;
	static int o=0;
	static St st;
	static void Main(){
		Sc sc=new Sc();
		int[] s=sc.Ia;
		int n=s[0],m=n-1;
		li=new List<Tuple<int,int,int>>[n+1];
		li2=new List<Tuple<int,int>>[n+1];
		b=new bool[n+1];
		h=new int[(n<<1)-1];
		ix=new int[n+1];
		ans=new int[s[1]];
		di=new int[n+1];
		c1=new int[n+1];
		c2=new int[n+1];
		z=new int[s[1]][];
		for(int i=1;i<=n;i++){
			li[i]=new List<Tuple<int,int,int>>();
			li2[i]=new List<Tuple<int,int>>();
		}
		for(int i=0;i<m;i++){
			int[] e=sc.Ia;
			li[e[0]].Add(Tuple.Create(e[1],e[2],e[3]));
			li[e[1]].Add(Tuple.Create(e[0],e[2],e[3]));
		}
		st=new St(n<<1,false);
		Fu1(1,1,0);
		for(int i = 0;i<s[1];i++) {
			z[i]=sc.Ia;
			int d=Lca(z[i][2],z[i][3]);
			ans[i]=di[z[i][2]]+di[z[i][3]]-di[d]*2;
			li2[z[i][2]].Add(Tuple.Create(i,1));
			li2[z[i][3]].Add(Tuple.Create(i,1));
			li2[d].Add(Tuple.Create(i,-2));
		}
		b=new bool[n+1];
		Fu2(1);
		Console.WriteLine(String.Join("\n",ans));
	}
	static void Fu2(int a){
		b[a]=true;
		for(int i=0;i<li2[a].Count;i++){
			ans[li2[a][i].Item1]+=c1[z[li2[a][i].Item1][0]]*z[li2[a][i].Item1][1]*li2[a][i].Item2;
			ans[li2[a][i].Item1]-=c2[z[li2[a][i].Item1][0]]*li2[a][i].Item2;
		}
		for(int i=0;i<li[a].Count;i++){
			if(!b[li[a][i].Item1]){
				c1[li[a][i].Item2]++;
				c2[li[a][i].Item2]+=li[a][i].Item3;
				Fu2(li[a][i].Item1);
				c1[li[a][i].Item2]--;
				c2[li[a][i].Item2]-=li[a][i].Item3;
			}
		}
	}
	static int Lca(int a,int b){return h[st.Get(Min(ix[a],ix[b]),Max(ix[a],ix[b])).n];}
	static void Fu1(int a,int g,int p){
		b[a]=true;
		di[a]=p;
		h[o]=a;
		st.Ud(o,g);
		ix[a]=o;
		o++;
		for(int i=0;i<li[a].Count;i++){
			if(!b[li[a][i].Item1]){
				Fu1(li[a][i].Item1,g+1,p+li[a][i].Item3);
				h[o]=a;
				st.Ud(o,g);
				o++;
			}
		}
	}
}
public class St{
	public class Mo{
		public int n;
		public long d;
		public Mo(long d,int n){this.d=d;this.n=n;}
	}
	public Mo[] dat;
	private int m=1;
	private bool mm;
	private Mo du;
	private Func<Mo,Mo,bool> compare;
	public St(int n,bool mm){
		this.mm=mm;
		if(mm){du=new Mo(long.MinValue,-1);compare=CoMax;}
		else{du=new Mo(long.MaxValue,-1);compare=CoMin;}
		while(m<n){m<<=1;}
		dat=new Mo[m+n];
		for(int i=0;i<m+n;i++){dat[i]=du;}
	}
	private bool CoMax(Mo x,Mo y){return x.d>y.d;}
	private bool CoMin(Mo x,Mo y){return x.d<y.d;}
	public void Ud(int q,long b){
		q+=m-1;
		if(dat[q]==du){
			int z=q;
			dat[q]=new Mo(b,q-(m-1));
			while(q>0&&compare(dat[z],dat[(q-1)>>1])){
				dat[(q-1)>>1]=dat[z];
				q=(q-1)>>1;
			}
		}
		else{
			b+=dat[q].d;
			dat[q].d=du.d;
			dat[q]=new Mo(b,q-(m-1));
			q=(q-1)>>1;
			while(q>=0){
				Mo o=compare(dat[2*q+1],dat[2*q+2])?dat[2*q+1]:dat[2*q+2];
				if(dat[q]==o){break;}
				dat[q]=o;
				q=(q-1)>>1;
			}
		}
	}
	private Mo Fdg(int a,int b,int k,int l,int r){
		if(r<a||b<l){return du;}
		if(a<=l&&r<=b){return dat[k];}
		Mo p=Fdg(a,b,k*2+1,l,(l+r)>>1);
		Mo q=Fdg(a,b,k*2+2,(l+r+1)>>1,r);
		return compare(p,q)?p:q;
	}
	public Mo Get(int a,int b){return Fdg(a,b,0,0,m-1);}
}

public class Sc{
	public int I{get{return int.Parse(Console.ReadLine());}}
	public long L{get{return long.Parse(Console.ReadLine());}}
	public double D{get{return double.Parse(Console.ReadLine());}}
	public string S{get{return Console.ReadLine();}}
	public int[] Ia{get{return Array.ConvertAll(Console.ReadLine().Split(),int.Parse);}}
	public long[] La{get{return Array.ConvertAll(Console.ReadLine().Split(),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Console.ReadLine().Split(),double.Parse);}}
	public string[] Sa{get{return Console.ReadLine().Split();}}
	public object[] Oa{get{return Console.ReadLine().Split();}}
	public int[] Ia2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),int.Parse);}}
	public int[] Ia3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),int.Parse);}
	public int[] Ia3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),int.Parse);}
	public long[] La2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),long.Parse);}}
	public long[] La3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),long.Parse);}
	public long[] La3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),long.Parse);}
	public T[] Arr<T>(int n,Func<T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f();}return a;}
	public T[] Arr<T>(int n,Func<int,T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i);}return a;}
	public T[] Arr<T>(int n,Func<string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(Console.ReadLine().Split());}return a;}
	public T[] Arr<T>(int n,Func<int,string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i,Console.ReadLine().Split());}return a;}
}