#include<bits/stdc++.h>
#define debug(x) cerr<<"\tDEBUG: "<<#x<<" = "<<(x)<<endl
#define debug2(a,x) cerr<<#a<<"\tDEBUG: "<<#x<<" = "<<(x)<<endl
using namespace std;
const int maxn=1e5+100,maxm=maxn*40,P=1e9+7;
int tot,head[maxn],to[maxn<<1],nxt[maxn<<1],col[maxn<<1],w[maxn<<1];
void add_edge(int u,int v,int c,int d){
	to[++tot]=v;
	nxt[tot]=head[u];
	col[tot]=c;
	w[tot]=d;
	head[u]=tot;
}
int n,q;
int id,rt[maxn],lson[maxm],rson[maxm],sum[maxm],cnt[maxm];
int fa[maxn][20];
int dep[maxn];
void insert(int &rt,int l,int r,int x,int d){
	if(!rt)rt=++id;
	cnt[rt]++;
	sum[rt]+=d;
	if(l==r)return;
	int mid=l+r>>1;
	if(x<=mid)insert(lson[rt],l,mid,x,d);
	else insert(rson[rt],mid+1,r,x,d);
}
int merge(int a,int b,int l,int r){
	if(!a||!b)return a|b;
	int p=++id;
	cnt[p]=cnt[a]+cnt[b];
	sum[p]=sum[a]+sum[b];
	if(l==r)return p;
	int mid=l+r>>1;
	lson[p]=merge(lson[a],lson[b],l,mid);
	rson[p]=merge(rson[a],rson[b],mid+1,r);
	return p;
}
void dfs(int f,int x){
	fa[x][0]=f;
	dep[x]=dep[f]+1;
	for(int i=1;i<17;i++)
		fa[x][i]=fa[fa[x][i-1]][i-1];
	for(int i=head[x];i;i=nxt[i]){
		int y=to[i];
		if(y==f)continue;
//		puts("?");
		insert(rt[y],1,n-1,col[i],w[i]);
		rt[y]=merge(rt[y],rt[x],1,n-1);
		dfs(x,y);
	}
}
void up(int &a,int k){
	for(int i=0;i<17;i++)
		if(1<<i&k)a=fa[a][i];
}
int LCA(int a,int b){
	if(dep[a]<dep[b])swap(a,b);
	up(a,dep[a]-dep[b]);
	if(a==b)return a;
	for(int i=16;i>=0;i--)
		if(fa[a][i]!=fa[b][i])
			a=fa[a][i],b=fa[b][i];
	return fa[a][0];
}
int Cnt,Sum;
void Query(int rt,int l,int r,int x,int p){
	if(!rt)return;
	if(l==r){
		Cnt+=cnt[rt]*p;
		Sum+=sum[rt]*p;
		return;
	}
	int mid=l+r>>1;
	if(x<=mid)Query(lson[rt],l,mid,x,p);
	else Query(rson[rt],mid+1,r,x,p);
}
int main(){
	cin>>n>>q;
	for(int i=1,x,y,z,c;i<n;i++){
		scanf("%d%d%d%d",&x,&y,&c,&z);
		add_edge(x,y,c,z);
		add_edge(y,x,c,z);
	}
	dfs(0,1);
	for(int i=1,x,y,u,v;i<=q;i++){
		scanf("%d%d%d%d",&x,&y,&u,&v);
		int lca=LCA(u,v);
		int d=sum[rt[u]]+sum[rt[v]]-sum[rt[lca]]*2;
		Cnt=0,Sum=0;
		Query(rt[u],1,n-1,x,1);
		Query(rt[v],1,n-1,x,1);
		Query(rt[lca],1,n-1,x,-2);
//		debug(d);
		printf("%d\n",d-Sum+Cnt*y);
	}
    return 0;
}
### Prompt

In CPP, your task is to solve the following 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

### Response

```cpp
#include<bits/stdc++.h>
#define debug(x) cerr<<"\tDEBUG: "<<#x<<" = "<<(x)<<endl
#define debug2(a,x) cerr<<#a<<"\tDEBUG: "<<#x<<" = "<<(x)<<endl
using namespace std;
const int maxn=1e5+100,maxm=maxn*40,P=1e9+7;
int tot,head[maxn],to[maxn<<1],nxt[maxn<<1],col[maxn<<1],w[maxn<<1];
void add_edge(int u,int v,int c,int d){
	to[++tot]=v;
	nxt[tot]=head[u];
	col[tot]=c;
	w[tot]=d;
	head[u]=tot;
}
int n,q;
int id,rt[maxn],lson[maxm],rson[maxm],sum[maxm],cnt[maxm];
int fa[maxn][20];
int dep[maxn];
void insert(int &rt,int l,int r,int x,int d){
	if(!rt)rt=++id;
	cnt[rt]++;
	sum[rt]+=d;
	if(l==r)return;
	int mid=l+r>>1;
	if(x<=mid)insert(lson[rt],l,mid,x,d);
	else insert(rson[rt],mid+1,r,x,d);
}
int merge(int a,int b,int l,int r){
	if(!a||!b)return a|b;
	int p=++id;
	cnt[p]=cnt[a]+cnt[b];
	sum[p]=sum[a]+sum[b];
	if(l==r)return p;
	int mid=l+r>>1;
	lson[p]=merge(lson[a],lson[b],l,mid);
	rson[p]=merge(rson[a],rson[b],mid+1,r);
	return p;
}
void dfs(int f,int x){
	fa[x][0]=f;
	dep[x]=dep[f]+1;
	for(int i=1;i<17;i++)
		fa[x][i]=fa[fa[x][i-1]][i-1];
	for(int i=head[x];i;i=nxt[i]){
		int y=to[i];
		if(y==f)continue;
//		puts("?");
		insert(rt[y],1,n-1,col[i],w[i]);
		rt[y]=merge(rt[y],rt[x],1,n-1);
		dfs(x,y);
	}
}
void up(int &a,int k){
	for(int i=0;i<17;i++)
		if(1<<i&k)a=fa[a][i];
}
int LCA(int a,int b){
	if(dep[a]<dep[b])swap(a,b);
	up(a,dep[a]-dep[b]);
	if(a==b)return a;
	for(int i=16;i>=0;i--)
		if(fa[a][i]!=fa[b][i])
			a=fa[a][i],b=fa[b][i];
	return fa[a][0];
}
int Cnt,Sum;
void Query(int rt,int l,int r,int x,int p){
	if(!rt)return;
	if(l==r){
		Cnt+=cnt[rt]*p;
		Sum+=sum[rt]*p;
		return;
	}
	int mid=l+r>>1;
	if(x<=mid)Query(lson[rt],l,mid,x,p);
	else Query(rson[rt],mid+1,r,x,p);
}
int main(){
	cin>>n>>q;
	for(int i=1,x,y,z,c;i<n;i++){
		scanf("%d%d%d%d",&x,&y,&c,&z);
		add_edge(x,y,c,z);
		add_edge(y,x,c,z);
	}
	dfs(0,1);
	for(int i=1,x,y,u,v;i<=q;i++){
		scanf("%d%d%d%d",&x,&y,&u,&v);
		int lca=LCA(u,v);
		int d=sum[rt[u]]+sum[rt[v]]-sum[rt[lca]]*2;
		Cnt=0,Sum=0;
		Query(rt[u],1,n-1,x,1);
		Query(rt[v],1,n-1,x,1);
		Query(rt[lca],1,n-1,x,-2);
//		debug(d);
		printf("%d\n",d-Sum+Cnt*y);
	}
    return 0;
}
```