#include <bits/stdc++.h>
#define maxn 100005
using namespace std;
struct Node{
    int to,next,val,col;
}q[maxn<<1];
struct Query{
    int id,col,dis,tag;
    Query(){}
    Query(int _id,int _col,int _dis,int _tag){
        id=_id,col=_col,dis=_dis,tag=_tag;
    }
};
vector<Query>vec[maxn];
int head[maxn],cnt=0;
void add_edge(int from,int to,int col,int val){
    q[cnt].to=to;
    q[cnt].val=val;
    q[cnt].next=head[from];
    q[cnt].col=col;
    head[from]=cnt++;
}
struct LCA{
#define LOG 20
    int ST[maxn<<1][LOG];
    int val[maxn<<1],depth[maxn<<1],first[maxn<<1],len;
    int cal(int x,int y){
        return depth[x]<depth[y]?x:y;
    }
    void dfs(int x,int fa,int dis){
        val[++len]=x,depth[len]=dis;
        first[x]=len;
        for(int i=head[x];i!=-1;i=q[i].next){
            int to=q[i].to;
            if(to==fa) continue;
            dfs(to,x,dis+1);
            val[++len]=x;
            depth[len]=dis;
        }
    }
    void init(int root){
        len=0;
        dfs(root,-1,1);
        for(int i=1;i<=len;i++) ST[i][0]=i;
        for(int j=1;(1<<j)<=len;j++){
            for(int i=1;i+(1<<j)-1<=len;i++){
                ST[i][j]=cal(ST[i][j-1],ST[i+(1<<(j-1))][j-1]);
            }
        }
    }
    int query(int x,int y){
        int l=first[x],r=first[y];
        if(l>r) swap(l,r);
        int k=log2(r-l+1);
        return val[cal(ST[l][k],ST[r-(1<<k)+1][k])];
    }
}lca;
int res[maxn],dis[maxn],Cnt[maxn];
void dfs(int x,int fa,int d){
    for(auto it:vec[x]){
        res[it.id]+=it.tag*(d-dis[it.col]+Cnt[it.col]*it.dis);
    }
    for(int i=head[x];i!=-1;i=q[i].next){
        int to=q[i].to;
        if(to==fa) continue;
        Cnt[q[i].col]++;dis[q[i].col]+=q[i].val;
        dfs(to,x,q[i].val+d);
        Cnt[q[i].col]--,dis[q[i].col]-=q[i].val;
    }
}
int main()
{
    int n,Q;
    memset(head,-1,sizeof(head));
    cnt=0;
    scanf("%d%d",&n,&Q);
    for(int i=1;i<n;i++){
        int from,to,cal,val;
        scanf("%d%d%d%d",&from,&to,&cal,&val);
        add_edge(from,to,cal,val);
        add_edge(to,from,cal,val);
    }
    lca.init(1);
    for(int i=1;i<=Q;i++){
        int cal,dis,from,to;
        scanf("%d%d%d%d",&cal,&dis,&from,&to);
        vec[from].push_back(Query(i,cal,dis,1));
        vec[to].push_back(Query(i,cal,dis,1));
        int LCA=lca.query(from,to);
        vec[LCA].push_back(Query(i,cal,dis,-2));
    }
    dfs(1,0,0);
    for(int i=1;i<=Q;i++){
        printf("%d\n",res[i]);
    }
    return 0;
}
### Prompt

Please provide a CPP coded solution to the problem described below:

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 maxn 100005
using namespace std;
struct Node{
    int to,next,val,col;
}q[maxn<<1];
struct Query{
    int id,col,dis,tag;
    Query(){}
    Query(int _id,int _col,int _dis,int _tag){
        id=_id,col=_col,dis=_dis,tag=_tag;
    }
};
vector<Query>vec[maxn];
int head[maxn],cnt=0;
void add_edge(int from,int to,int col,int val){
    q[cnt].to=to;
    q[cnt].val=val;
    q[cnt].next=head[from];
    q[cnt].col=col;
    head[from]=cnt++;
}
struct LCA{
#define LOG 20
    int ST[maxn<<1][LOG];
    int val[maxn<<1],depth[maxn<<1],first[maxn<<1],len;
    int cal(int x,int y){
        return depth[x]<depth[y]?x:y;
    }
    void dfs(int x,int fa,int dis){
        val[++len]=x,depth[len]=dis;
        first[x]=len;
        for(int i=head[x];i!=-1;i=q[i].next){
            int to=q[i].to;
            if(to==fa) continue;
            dfs(to,x,dis+1);
            val[++len]=x;
            depth[len]=dis;
        }
    }
    void init(int root){
        len=0;
        dfs(root,-1,1);
        for(int i=1;i<=len;i++) ST[i][0]=i;
        for(int j=1;(1<<j)<=len;j++){
            for(int i=1;i+(1<<j)-1<=len;i++){
                ST[i][j]=cal(ST[i][j-1],ST[i+(1<<(j-1))][j-1]);
            }
        }
    }
    int query(int x,int y){
        int l=first[x],r=first[y];
        if(l>r) swap(l,r);
        int k=log2(r-l+1);
        return val[cal(ST[l][k],ST[r-(1<<k)+1][k])];
    }
}lca;
int res[maxn],dis[maxn],Cnt[maxn];
void dfs(int x,int fa,int d){
    for(auto it:vec[x]){
        res[it.id]+=it.tag*(d-dis[it.col]+Cnt[it.col]*it.dis);
    }
    for(int i=head[x];i!=-1;i=q[i].next){
        int to=q[i].to;
        if(to==fa) continue;
        Cnt[q[i].col]++;dis[q[i].col]+=q[i].val;
        dfs(to,x,q[i].val+d);
        Cnt[q[i].col]--,dis[q[i].col]-=q[i].val;
    }
}
int main()
{
    int n,Q;
    memset(head,-1,sizeof(head));
    cnt=0;
    scanf("%d%d",&n,&Q);
    for(int i=1;i<n;i++){
        int from,to,cal,val;
        scanf("%d%d%d%d",&from,&to,&cal,&val);
        add_edge(from,to,cal,val);
        add_edge(to,from,cal,val);
    }
    lca.init(1);
    for(int i=1;i<=Q;i++){
        int cal,dis,from,to;
        scanf("%d%d%d%d",&cal,&dis,&from,&to);
        vec[from].push_back(Query(i,cal,dis,1));
        vec[to].push_back(Query(i,cal,dis,1));
        int LCA=lca.query(from,to);
        vec[LCA].push_back(Query(i,cal,dis,-2));
    }
    dfs(1,0,0);
    for(int i=1;i<=Q;i++){
        printf("%d\n",res[i]);
    }
    return 0;
}
```