#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll, ll> P;

#define fi first
#define se second
#define repl(i,a,b) for(ll i=(ll)(a);i<(ll)(b);i++)
#define rep(i,n) repl(i,0,n)
#define all(x) (x).begin(),(x).end()
#define dbg(x) cout<<#x"="<<x<<endl
#define mmax(x,y) (x>y?x:y)
#define mmin(x,y) (x<y?x:y)
#define maxch(x,y) x=mmax(x,y)
#define minch(x,y) x=mmin(x,y)
#define uni(x) x.erase(unique(all(x)),x.end())
#define exist(x,y) (find(all(x),y)!=x.end())
#define bcnt __builtin_popcountll

#define INF 1e16
#define mod 1000000007

#define MAX_LOG_V 20
#define MAX_V 100010

struct edge{
  ll v,c,d;
};
struct query{
  ll idx,c,y;
  bool islca;
};

vector<edge> G[MAX_V];
vector<query> qs[MAX_V];
int root;

int V;

int parent[MAX_LOG_V][MAX_V];
int depth[MAX_V];

void dfs(int v,int p,int d){
  parent[0][v]=p;
  depth[v]=d;
  for(int i=0;i<(int)G[v].size();i++){
    if(G[v][i].v!=p)dfs(G[v][i].v,v,d+1);
  }
}

void init(){
  dfs(root,-1,0);
  for(int k=0;k+1<MAX_LOG_V;k++){
    for(int v=0;v<V;v++){
      if(parent[k][v]<0)parent[k+1][v]=-1;
      else parent[k+1][v]=parent[k][parent[k][v]];
    }
  }
}

int lca(int u,int v){
  if(depth[u]>depth[v])swap(u,v);
  for(int k=0;k<MAX_LOG_V;k++){
    if((depth[v]-depth[u])>>k&1){
      v=parent[k][v];
    }
  }
  if(u==v)return u;
  for(int k=MAX_LOG_V-1;k>=0;k--){
    if(parent[k][u]!=parent[k][v]){
      u=parent[k][u];
      v=parent[k][v];
    }
  }
  return parent[0][u];
}

ll colcnt[100010],colsum[100010];
ll res[100010];

void dfs2(ll v,ll pre,ll dep){
  for(edge e : G[v]){
    if(e.v==pre)continue;
    colcnt[e.c]++;
    colsum[e.c]+=e.d;
    dfs2(e.v,v,dep+e.d);
    colcnt[e.c]--;
    colsum[e.c]-=e.d;
  }

  for(query q : qs[v]){
    if(q.islca){
      res[q.idx]-=dep*2;
      res[q.idx]+=colsum[q.c]*2;
      res[q.idx]-=colcnt[q.c]*q.y*2;
    }else{
      res[q.idx]+=dep;
      res[q.idx]-=colsum[q.c];
      res[q.idx]+=colcnt[q.c]*q.y;
    }
  }
}

int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);

  int Q;
  cin>>V>>Q;
  rep(i,V-1){
    int a,b,c,d;
    cin>>a>>b>>c>>d;
    a--;b--; c--;
    G[a].push_back((edge){b,c,d});
    G[b].push_back((edge){a,c,d});
  }

  init();

  rep(i,Q){
    ll x,y,u,v;
    cin>>x>>y>>u>>v;
    x--;u--;v--;
    ll lc=lca(u,v);
    qs[u].push_back((query){i,x,y,false});
    qs[v].push_back((query){i,x,y,false});
    qs[lc].push_back((query){i,x,y,true});
  }

  dfs2(0,-1,0);

  rep(i,Q)cout<<res[i]<<endl;

  return 0;
}

### Prompt

Your challenge is to write a cpp solution to 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>
using namespace std;

typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll, ll> P;

#define fi first
#define se second
#define repl(i,a,b) for(ll i=(ll)(a);i<(ll)(b);i++)
#define rep(i,n) repl(i,0,n)
#define all(x) (x).begin(),(x).end()
#define dbg(x) cout<<#x"="<<x<<endl
#define mmax(x,y) (x>y?x:y)
#define mmin(x,y) (x<y?x:y)
#define maxch(x,y) x=mmax(x,y)
#define minch(x,y) x=mmin(x,y)
#define uni(x) x.erase(unique(all(x)),x.end())
#define exist(x,y) (find(all(x),y)!=x.end())
#define bcnt __builtin_popcountll

#define INF 1e16
#define mod 1000000007

#define MAX_LOG_V 20
#define MAX_V 100010

struct edge{
  ll v,c,d;
};
struct query{
  ll idx,c,y;
  bool islca;
};

vector<edge> G[MAX_V];
vector<query> qs[MAX_V];
int root;

int V;

int parent[MAX_LOG_V][MAX_V];
int depth[MAX_V];

void dfs(int v,int p,int d){
  parent[0][v]=p;
  depth[v]=d;
  for(int i=0;i<(int)G[v].size();i++){
    if(G[v][i].v!=p)dfs(G[v][i].v,v,d+1);
  }
}

void init(){
  dfs(root,-1,0);
  for(int k=0;k+1<MAX_LOG_V;k++){
    for(int v=0;v<V;v++){
      if(parent[k][v]<0)parent[k+1][v]=-1;
      else parent[k+1][v]=parent[k][parent[k][v]];
    }
  }
}

int lca(int u,int v){
  if(depth[u]>depth[v])swap(u,v);
  for(int k=0;k<MAX_LOG_V;k++){
    if((depth[v]-depth[u])>>k&1){
      v=parent[k][v];
    }
  }
  if(u==v)return u;
  for(int k=MAX_LOG_V-1;k>=0;k--){
    if(parent[k][u]!=parent[k][v]){
      u=parent[k][u];
      v=parent[k][v];
    }
  }
  return parent[0][u];
}

ll colcnt[100010],colsum[100010];
ll res[100010];

void dfs2(ll v,ll pre,ll dep){
  for(edge e : G[v]){
    if(e.v==pre)continue;
    colcnt[e.c]++;
    colsum[e.c]+=e.d;
    dfs2(e.v,v,dep+e.d);
    colcnt[e.c]--;
    colsum[e.c]-=e.d;
  }

  for(query q : qs[v]){
    if(q.islca){
      res[q.idx]-=dep*2;
      res[q.idx]+=colsum[q.c]*2;
      res[q.idx]-=colcnt[q.c]*q.y*2;
    }else{
      res[q.idx]+=dep;
      res[q.idx]-=colsum[q.c];
      res[q.idx]+=colcnt[q.c]*q.y;
    }
  }
}

int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);

  int Q;
  cin>>V>>Q;
  rep(i,V-1){
    int a,b,c,d;
    cin>>a>>b>>c>>d;
    a--;b--; c--;
    G[a].push_back((edge){b,c,d});
    G[b].push_back((edge){a,c,d});
  }

  init();

  rep(i,Q){
    ll x,y,u,v;
    cin>>x>>y>>u>>v;
    x--;u--;v--;
    ll lc=lca(u,v);
    qs[u].push_back((query){i,x,y,false});
    qs[v].push_back((query){i,x,y,false});
    qs[lc].push_back((query){i,x,y,true});
  }

  dfs2(0,-1,0);

  rep(i,Q)cout<<res[i]<<endl;

  return 0;
}

```