Problem: 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.

Example

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


Output

130
200
60

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
#define int long long
#define pii pair<int,int>
#define mp make_pair
int n,q;
struct edge{
	int v,c,w;
	edge(int vv,int cc,int ww){
		v=vv;
		c=cc;
		w=ww;
	}
};
vector<edge> G[123456];
int cnt[123456],in[123456],out[123456],tim=0;
int pa[18][123456];
bool anc(int x,int y){
	return in[x]<=in[y] && out[x]>=out[y];
}
void dfs(int cur,int pre){
	in[cur]=++tim;
	pa[0][cur]=pre;
	for(edge tmp:G[cur]){
		int nxt=tmp.v,col=tmp.c,w=tmp.w;
		if(nxt==pre) continue;
		dfs(nxt,cur);
	}
	out[cur]=++tim;
}
void build(){
	for(int i=1;i<18;i++)
		for(int j=1;j<=n;j++)
			pa[i][j]=pa[i-1][pa[i-1][j]];
}
int lca(int x,int y){
	if(anc(x,y)) return x;
	if(anc(y,x)) return y;
	for(int i=17;i>=0;i--)
		if(!anc(pa[i][x],y)) x=pa[i][x];
	return pa[0][x];
}
int ans[123456],q_col[123456],q_val[123456],dist[123456];
vector<int> query[123456];
void solve(int cur,int pre,int cur_dis){
	for(int id:query[cur]){
		int mul=1;
		if(id<0) mul=-2,id=-id;
		ans[id]+=mul*(cur_dis+cnt[q_col[id]]*q_val[id]-dist[q_col[id]]);
	}

	for(edge tmp:G[cur]){
		int nxt=tmp.v,col=tmp.c,w=tmp.w;
		if(nxt==pre) continue;
		cnt[col]++;
		dist[col]+=w;
		solve(nxt,cur,cur_dis+w);
		dist[col]-=w;
		cnt[col]--;
	}
}
int32_t main(){
	ios::sync_with_stdio();
	cin.tie(0);
	cin>>n>>q;
	for(int i=0;i<n-1;i++){
		int u,v,c,w;cin>>u>>v>>c>>w;
		G[u].push_back(edge(v,c,w));
		G[v].push_back(edge(u,c,w));
	}
	dfs(1,1);
	build();
	for(int i=1;i<=q;i++){
		int u,v;cin>>q_col[i]>>q_val[i]>>u>>v;
		query[u].push_back(i);
		query[v].push_back(i);
		query[lca(u,v)].push_back(-i);
	}
	solve(1,1,0);

	for(int i=1;i<=q;i++)
		cout<<ans[i]<<endl;
}