#pragma GCC optimize ("Ofast")
#include<bits/stdc++.h>
using namespace std;
void*wmem;
char memarr[96000000];
template<class S, class T> inline S min_L(S a,T b){
  return a<=b?a:b;
}
template<class S, class T> inline S max_L(S a,T b){
  return a>=b?a:b;
}
template<class T> inline void walloc1d(T **arr, int x, void **mem = &wmem){
  static int skip[16] = {0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1};
  (*mem) = (void*)( ((char*)(*mem)) + skip[((unsigned long long)(*mem)) & 15] );
  (*arr)=(T*)(*mem);
  (*mem)=((*arr)+x);
}
template<class T> inline void walloc1d(T **arr, int x1, int x2, void **mem = &wmem){
  walloc1d(arr, x2-x1, mem);
  (*arr) -= x1;
}
inline int my_getchar_unlocked(){
  static char buf[1048576];
  static int s = 1048576;
  static int e = 1048576;
  if(s == e && e == 1048576){
    e = fread_unlocked(buf, 1, 1048576, stdin);
    s = 0;
  }
  if(s == e){
    return EOF;
  }
  return buf[s++];
}
inline void rd(int &x){
  int k;
  int m=0;
  x=0;
  for(;;){
    k = my_getchar_unlocked();
    if(k=='-'){
      m=1;
      break;
    }
    if('0'<=k&&k<='9'){
      x=k-'0';
      break;
    }
  }
  for(;;){
    k = my_getchar_unlocked();
    if(k<'0'||k>'9'){
      break;
    }
    x=x*10+k-'0';
  }
  if(m){
    x=-x;
  }
}
inline void rd(long long &x){
  int k;
  int m=0;
  x=0;
  for(;;){
    k = my_getchar_unlocked();
    if(k=='-'){
      m=1;
      break;
    }
    if('0'<=k&&k<='9'){
      x=k-'0';
      break;
    }
  }
  for(;;){
    k = my_getchar_unlocked();
    if(k<'0'||k>'9'){
      break;
    }
    x=x*10+k-'0';
  }
  if(m){
    x=-x;
  }
}
inline int rd_int(void){
  int x;
  rd(x);
  return x;
}
struct MY_WRITER{
  char buf[1048576];
  int s;
  int e;
  MY_WRITER(){
    s = 0;
    e = 1048576;
  }
  ~MY_WRITER(){
    if(s){
      fwrite_unlocked(buf, 1, s, stdout);
    }
  }
}
;
MY_WRITER MY_WRITER_VAR;
void my_putchar_unlocked(int a){
  if(MY_WRITER_VAR.s == MY_WRITER_VAR.e){
    fwrite_unlocked(MY_WRITER_VAR.buf, 1, MY_WRITER_VAR.s, stdout);
    MY_WRITER_VAR.s = 0;
  }
  MY_WRITER_VAR.buf[MY_WRITER_VAR.s++] = a;
}
inline void wt_L(char a){
  my_putchar_unlocked(a);
}
inline void wt_L(long long x){
  int s=0;
  int m=0;
  char f[20];
  if(x<0){
    m=1;
    x=-x;
  }
  while(x){
    f[s++]=x%10;
    x/=10;
  }
  if(!s){
    f[s++]=0;
  }
  if(m){
    my_putchar_unlocked('-');
  }
  while(s--){
    my_putchar_unlocked(f[s]+'0');
  }
}
template<class S> inline void arrInsert(const int k, int &sz, S a[], const S aval){
  int i;
  sz++;
  for(i=sz-1;i>k;i--){
    a[i] = a[i-1];
  }
  a[k] = aval;
}
template<class S, class T> inline void arrInsert(const int k, int &sz, S a[], const S aval, T b[], const T bval){
  int i;
  sz++;
  for(i=sz-1;i>k;i--){
    a[i] = a[i-1];
  }
  for(i=sz-1;i>k;i--){
    b[i] = b[i-1];
  }
  a[k] = aval;
  b[k] = bval;
}
template<class S, class T, class U> inline void arrInsert(const int k, int &sz, S a[], const S aval, T b[], const T bval, U c[], const U cval){
  int i;
  sz++;
  for(i=sz-1;i>k;i--){
    a[i] = a[i-1];
  }
  for(i=sz-1;i>k;i--){
    b[i] = b[i-1];
  }
  for(i=sz-1;i>k;i--){
    c[i] = c[i-1];
  }
  a[k] = aval;
  b[k] = bval;
  c[k] = cval;
}
template<class S, class T, class U, class V> inline void arrInsert(const int k, int &sz, S a[], const S aval, T b[], const T bval, U c[], const U cval, V d[], const V dval){
  int i;
  sz++;
  for(i=sz-1;i>k;i--){
    a[i] = a[i-1];
  }
  for(i=sz-1;i>k;i--){
    b[i] = b[i-1];
  }
  for(i=sz-1;i>k;i--){
    c[i] = c[i-1];
  }
  for(i=sz-1;i>k;i--){
    d[i] = d[i-1];
  }
  a[k] = aval;
  b[k] = bval;
  c[k] = cval;
  d[k] = dval;
}
template<class S, class T> inline S chmin(S &a, T b){
  if(a>b){
    a=b;
  }
  return a;
}
template <class T> struct DijkstraHeap{
  int*hp;
  int*place;
  int size;
  char*visited;
  T*val;
  void malloc(int N){
    hp = (int*)std::malloc(N*sizeof(int));
    place = (int*)std::malloc(N*sizeof(int));
    visited = (char*)std::malloc(N*sizeof(char));
    val = (T*)std::malloc(N*sizeof(T));
  }
  void free(){
    std::free(hp);
    std::free(place);
    std::free(visited);
    std::free(val);
  }
  void walloc(int N, void **mem=&wmem){
    walloc1d(&hp, N, mem);
    walloc1d(&place, N, mem);
    walloc1d(&visited, N, mem);
    walloc1d(&val, N, mem);
  }
  void init(int N){
    int i;
    size = 0;
    for(i=(0);i<(N);i++){
      place[i]=-1;
    }
    for(i=(0);i<(N);i++){
      visited[i]=0;
    }
  }
  void up(int n){
    int m;
    while(n){
      m=(n-1)/2;
      if(val[hp[m]]<=val[hp[n]]){
        break;
      }
      swap(hp[m],hp[n]);
      swap(place[hp[m]],place[hp[n]]);
      n=m;
    }
  }
  void down(int n){
    int m;
    for(;;){
      m=2*n+1;
      if(m>=size){
        break;
      }
      if(m+1<size&&val[hp[m]]>val[hp[m+1]]){
        m++;
      }
      if(val[hp[m]]>=val[hp[n]]){
        break;
      }
      swap(hp[m],hp[n]);
      swap(place[hp[m]],place[hp[n]]);
      n=m;
    }
  }
  void change(int n, T v){
    if(visited[n]||(place[n]>=0&&val[n]<=v)){
      return;
    }
    val[n]=v;
    if(place[n]==-1){
      place[n]=size;
      hp[size++]=n;
      up(place[n]);
    }
    else{
      up(place[n]);
    }
  }
  int pop(void){
    int res=hp[0];
    place[res]=-1;
    size--;
    if(size){
      hp[0]=hp[size];
      place[hp[0]]=0;
      down(0);
    }
    visited[res]=1;
    return res;
  }
}
;
template<class T> struct segtree{
  int N;
  int logN;
  T*sum;
  T*mn;
  int*mnind;
  T*fixval;
  char*fixed;
  T*addval;
  void malloc(int maxN, int once = 0){
    int i;
    for(i=1;i<maxN;i*=2){
      ;
    }
    sum = new T[2*i];
    mn = new T[2*i];
    mnind = new int[2*i];
    fixval = new T[i];
    addval = new T[i];
    fixed = new char[i];
    if(once){
      setN(maxN);
    }
  }
  void walloc(int maxN, int once = 0, void **mem = &wmem){
    int i;
    for(i=1;i<maxN;i*=2){
      ;
    }
    walloc1d(&sum, 2*i, mem);
    walloc1d(&mn, 2*i, mem);
    walloc1d(&mnind, 2*i, mem);
    walloc1d(&fixval, i, mem);
    walloc1d(&addval, i, mem);
    walloc1d(&fixed, i, mem);
    if(once){
      setN(maxN);
    }
  }
  void free(void){
    delete [] sum;
    delete [] mn;
    delete [] mnind;
    delete [] fixval;
    delete [] addval;
    delete [] fixed;
  }
  T& operator[](int i){
    return sum[N+i];
  }
  void setN(int n, int zerofill = 1, int dobuild = 1){
    int i;
    for(i=1,logN=0;i<n;i*=2,logN++){
      ;
    }
    N = i;
    if(zerofill){
      for(i=(0);i<(N);i++){
        sum[N+i] = 0;
      }
    }
    if(dobuild){
      build();
    }
  }
  void build(void){
    int i;
    for(i=(0);i<(N);i++){
      mn[N+i] = sum[N+i];
      mnind[N+i] = i;
    }
    for(i=N-1;i;i--){
      sum[i] = sum[2*i] + sum[2*i+1];
      if(mn[2*i] <= mn[2*i+1]){
        mn[i] = mn[2*i];
        mnind[i] = mnind[2*i];
      }
      else{
        mn[i] = mn[2*i+1];
        mnind[i] = mnind[2*i+1];
      }
    }
    int o0VCpjj8 = N;
    for(i=(1);i<(o0VCpjj8);i++){
      fixed[i] = 0;
    }
    int vzsjNTAU = N;
    for(i=(1);i<(vzsjNTAU);i++){
      addval[i] = 0;
    }
  }
  inline void push_one(int a, int sz, int st){
    if(fixed[a]){
      if(sz > 1){
        fixed[a*2] = fixed[a*2+1] = 1;
        fixval[a*2] = fixval[a*2+1] = fixval[a];
        sum[a*2] = sum[a*2+1] = sz * fixval[a];
        mn[a*2] = mn[a*2+1] = fixval[a];
        mnind[a*2] = st;
        mnind[a*2+1] = st + sz;
      }
      else{
        sum[a*2] = sum[a*2+1] = sz * fixval[a];
        mn[a*2] = mn[a*2+1] = fixval[a];
        mnind[a*2] = st;
        mnind[a*2+1] = st + sz;
      }
      fixed[a] = 0;
      addval[a] = 0;
      return;
    }
    if(addval[a] != 0){
      if(sz > 1){
        if(fixed[a*2]){
          fixval[a*2] += addval[a];
        }
        else{
          addval[a*2] += addval[a];
        }
        if(fixed[a*2+1]){
          fixval[a*2+1] += addval[a];
        }
        else{
          addval[a*2+1] += addval[a];
        }
        sum[a*2] += sz * addval[a];
        sum[a*2+1] += sz * addval[a];
        mn[a*2] += addval[a];
        mn[a*2+1] += addval[a];
      }
      else{
        sum[a*2] += sz * addval[a];
        sum[a*2+1] += sz * addval[a];
        mn[a*2] += addval[a];
        mn[a*2+1] += addval[a];
      }
      addval[a] = 0;
      return;
    }
  }
  inline void push(int a){
    int i;
    int aa = a - N;
    int nd;
    int sz;
    int st;
    for(i=logN;i;i--){
      nd = a>>i;
      sz = 1<<(i-1);
      st = 2 * sz * (aa>>i);
      push_one(nd, sz, st);
    }
  }
  inline void build(int a){
    int sz = 1;
    int st = a - N;
    while(a > 1){
      if(a%2){
        st += sz;
      }
      a /= 2;
      sz *= 2;
      if(fixed[a]){
        sum[a] = sz * fixval[a];
        mn[a] = fixval[a];
      }
      else{
        sum[a] = sum[a*2] + sum[a*2+1];
        if(mn[a*2] <= mn[a*2+1]){
          mn[a] = mn[a*2];
          mnind[a] = mnind[a*2];
        }
        else{
          mn[a] = mn[a*2+1];
          mnind[a] = mnind[a*2+1];
        }
        if(addval[a] != 0){
          mn[a] += addval[a];
          sum[a] += sz * addval[a];
        }
      }
    }
  }
  inline void change(int a, int b, T val){
    int sz = 1;
    int aa;
    int bb;
    int st_a = a;
    int st_b = b;
    if(a >= b){
      return;
    }
    aa = (a += N);
    bb = (b += N);
    push(a);
    push(b-1);
    if(a%2){
      sum[a] = mn[a] = val;
      a++;
      st_a += sz;
    }
    if(b%2){
      b--;
      st_b -= sz;
      sum[b] = mn[b] = val;
    }
    a /= 2;
    b /= 2;
    while(a < b){
      sz *= 2;
      if(a%2){
        fixed[a]=1;
        fixval[a]=val;
        sum[a] = sz * val;
        mn[a] = val;
        mnind[a] = st_a;
        a++;
        st_a += sz;
      }
      if(b%2){
        b--;
        st_b -= sz;
        fixed[b]=1;
        fixval[b]=val;
        sum[b] = sz * val;
        mn[b] = val;
        mnind[b] = st_b;
      }
      a /= 2;
      b /= 2;
    }
    build(aa);
    build(bb-1);
  }
  inline void add(int a, int b, T val){
    int sz = 1;
    int aa;
    int bb;
    if(a >= b){
      return;
    }
    aa = (a += N);
    bb = (b += N);
    push(a);
    push(b-1);
    if(a%2){
      sum[a] += val;
      mn[a] += val;
      a++;
    }
    if(b%2){
      b--;
      sum[b] += val;
      mn[b] += val;
    }
    a /= 2;
    b /= 2;
    while(a < b){
      sz *= 2;
      if(a%2){
        if(fixed[a]){
          fixval[a] += val;
        }
        else{
          addval[a] += val;
        }
        sum[a] += sz * val;
        mn[a] += val;
        a++;
      }
      if(b%2){
        b--;
        if(fixed[b]){
          fixval[b] += val;
        }
        else{
          addval[b] += val;
        }
        sum[b] += sz * val;
        mn[b] += val;
      }
      a /= 2;
      b /= 2;
    }
    build(aa);
    build(bb-1);
  }
  inline pair<T,int> getMin(int a, int b){
    pair<T,int> res;
    pair<T,int> tmp;
    int fga = 0;
    int fgb = 0;
    a += N;
    b += N;
    push(a);
    push(b-1);
    while(a < b){
      if(a%2){
        if(fga){
          res =min_L(res, make_pair(mn[a], mnind[a]));
        }
        else{
          res = make_pair(mn[a], mnind[a]);
          fga = 1;
        }
        a++;
      }
      if(b%2){
        b--;
        if(fgb){
          tmp =min_L(make_pair(mn[b], mnind[b]), tmp);
        }
        else{
          tmp = make_pair(mn[b], mnind[b]);
          fgb = 1;
        }
      }
      a /= 2;
      b /= 2;
    }
    if(fga==1 && fgb==0){
      return res;
    }
    if(fga==0 && fgb==1){
      return tmp;
    }
    if(fga==1 && fgb==1){
      res =min_L(res, tmp);
      return res;
    }
    return res;
  }
  inline T getMinVal(int a, int b){
    T res;
    T tmp;
    int fga = 0;
    int fgb = 0;
    a += N;
    b += N;
    push(a);
    push(b-1);
    while(a < b){
      if(a%2){
        if(fga){
          res =min_L(res, mn[a]);
        }
        else{
          res = mn[a];
          fga = 1;
        }
        a++;
      }
      if(b%2){
        b--;
        if(fgb){
          tmp =min_L(mn[b], tmp);
        }
        else{
          tmp = mn[b];
          fgb = 1;
        }
      }
      a /= 2;
      b /= 2;
    }
    if(fga==1 && fgb==0){
      return res;
    }
    if(fga==0 && fgb==1){
      return tmp;
    }
    if(fga==1 && fgb==1){
      res =min_L(res, tmp);
      return res;
    }
    return res;
  }
  inline int getMinInd(int a, int b){
    return getMin(a,b).second;
  }
  inline T getSum(int a, int b){
    T res;
    T tmp;
    int fga = 0;
    int fgb = 0;
    a += N;
    b += N;
    push(a);
    push(b-1);
    while(a < b){
      if(a%2){
        if(fga){
          res = res + sum[a];
        }
        else{
          res = sum[a];
          fga = 1;
        }
        a++;
      }
      if(b%2){
        b--;
        if(fgb){
          tmp = sum[b] + tmp;
        }
        else{
          tmp = sum[b];
          fgb = 1;
        }
      }
      a /= 2;
      b /= 2;
    }
    if(fga==1 && fgb==0){
      return res;
    }
    if(fga==0 && fgb==1){
      return tmp;
    }
    if(fga==1 && fgb==1){
      res = res + tmp;
      return res;
    }
    return res;
  }
}
;
struct graph{
  int N;
  int*es;
  int**edge;
  void setEdge(int N__, int M, int A[], int B[], void **mem = &wmem){
    int i;
    N = N__;
    walloc1d(&es, N, mem);
    walloc1d(&edge, N, mem);
    for(i=(0);i<(N);i++){
      es[i] = 0;
    }
    for(i=(0);i<(M);i++){
      es[A[i]]++;
      es[B[i]]++;
    }
    for(i=(0);i<(N);i++){
      walloc1d(&edge[i], es[i], mem);
    }
    for(i=(0);i<(N);i++){
      es[i] = 0;
    }
    for(i=(0);i<(M);i++){
      edge[A[i]][es[A[i]]++] = B[i];
      edge[B[i]][es[B[i]]++] = A[i];
    }
  }
  void getDist(int root, int res[], void *mem = wmem){
    int i;
    int j;
    int k;
    int*q;
    int s;
    int z;
    walloc1d(&q, N, &mem);
    for(i=(0);i<(N);i++){
      res[i]=-1;
    }
    res[root]=0;
    s=0;
    z=1;
    q[0]=root;
    while(z){
      i=q[s++];
      z--;
      for(j=(0);j<(es[i]);j++){
        k=edge[i][j];
        if(res[k]>=0){
          continue;
        }
        res[k]=res[i]+1;
        q[s+z++]=k;
      }
    }
  }
  int getDist(int a, int b, void *mem = wmem){
    int i;
    int j;
    int k;
    int*q;
    int s;
    int z;
    int*d;
    if(a==b){
      return 0;
    }
    walloc1d(&d, N, &mem);
    walloc1d(&q, N, &mem);
    for(i=(0);i<(N);i++){
      d[i] = -1;
    }
    d[a] = 0;
    s = 0;
    z = 1;
    q[0] = a;
    while(z){
      i = q[s++];
      z--;
      for(j=(0);j<(es[i]);j++){
        k = edge[i][j];
        if(d[k] >= 0){
          continue;
        }
        d[k] = d[i] + 1;
        if(k==b){
          return d[k];
        }
        q[s+z++] = k;
      }
    }
    return -1;
  }
}
;
template<class T> struct wgraph{
  int N;
  int*es;
  int**edge;
  T**cost;
  graph g;
  void setEdge(int N__, int M, int A[], int B[], T C[], void **mem = &wmem){
    int i;
    N = N__;
    walloc1d(&es, N, mem);
    for(i=(0);i<(N);i++){
      es[i] = 0;
    }
    for(i=(0);i<(M);i++){
      es[A[i]]++;
      es[B[i]]++;
    }
    walloc1d(&edge, N, mem);
    for(i=(0);i<(N);i++){
      walloc1d(&edge[i], es[i], mem);
    }
    walloc1d(&cost, N, mem);
    for(i=(0);i<(N);i++){
      walloc1d(&cost[i], es[i], mem);
    }
    for(i=(0);i<(N);i++){
      es[i] = 0;
    }
    for(i=(0);i<(M);i++){
      edge[A[i]][es[A[i]]] = B[i];
      edge[B[i]][es[B[i]]] = A[i];
      cost[A[i]][es[A[i]]++] = C[i];
      cost[B[i]][es[B[i]]++] = C[i];
    }
    g.N = N;
    g.es = es;
    g.edge = edge;
  }
  template<class S> void getDist(int root, S res[], S unreachable = -1, void *mem = wmem){
    int i;
    int j;
    DijkstraHeap<S> hp;
    hp.walloc(N, &mem);
    hp.init(N);
    hp.change(root,0);
    while(hp.size){
      i = hp.pop();
      for(j=(0);j<(es[i]);j++){
        hp.change(edge[i][j], hp.val[i]+cost[i][j]);
      }
    }
    for(i=(0);i<(N);i++){
      res[i] = (hp.visited[i] ? hp.val[i] : unreachable);
    }
  }
}
;
struct HLD{
  int N;
  int*es;
  int**edge;
  int*group;
  int*groupind;
  int groupNum;
  int*groupSize;
  int**groupNode;
  int*groupUpNode;
  int*groupDepth;
  void init(graph g, void **mem = &wmem){
    init(g.N, g.es, g.edge, mem);
  }
  void init(int N__, int *es__, int **edge__, void **mem = &wmem){
    int i;
    int j;
    int k;
    int x;
    int y;
    int mx;
    int*q;
    int q_st;
    int q_ed;
    int*sz;
    char*vis;
    void*tmpmem;
    N = N__;
    es = es__;
    edge = edge__;
    walloc1d(&group, N, mem);
    walloc1d(&groupind, N, mem);
    tmpmem = *mem;
    walloc1d(&q, N, &tmpmem);
    walloc1d(&sz, N, &tmpmem);
    walloc1d(&vis, N, &tmpmem);
    for(i=(0);i<(N);i++){
      vis[i] = 0;
    }
    q_st = 0;
    q_ed = 1;
    q[0] = 0;
    vis[0] = 1;
    while(q_st < q_ed){
      i = q[q_st++];
      for(j=(0);j<(es[i]);j++){
        k = edge[i][j];
        if(!vis[k]){
          vis[k] = 1;
          q[q_ed++] = k;
        }
      }
    }
    for(i=(0);i<(N);i++){
      sz[i] = 0;
    }
    for(j=N-1;j>=0;j--){
      i = q[j];
      sz[i] = 1;
      for(k=(0);k<(es[i]);k++){
        sz[i] += sz[edge[i][k]];
      }
    }
    for(i=(0);i<(N);i++){
      group[i] = -1;
    }
    groupNum = 0;
    for(j=(0);j<(N);j++){
      i = q[j];
      if(group[i]>=0){
        continue;
      }
      group[i] = groupNum++;
      groupind[i] = 0;
      for(;;){
        mx = -1;
        for(k=(0);k<(es[i]);k++){
          if(group[edge[i][k]] != -1){
            continue;
          }
          if(mx==-1){
            mx = k;
          }
          else if(sz[edge[i][k]] > sz[edge[i][mx]]){
            mx = k;
          }
        }
        if(mx==-1){
          break;
        }
        group[edge[i][mx]] = group[i];
        groupind[edge[i][mx]] = groupind[i]+1;
        i = edge[i][mx];
      }
    }
    walloc1d(&groupSize, groupNum, mem);
    walloc1d(&groupUpNode, groupNum, mem);
    walloc1d(&groupDepth, groupNum, mem);
    for(i=(0);i<(groupNum);i++){
      groupSize[i] = 0;
    }
    for(i=(0);i<(N);i++){
      groupSize[group[i]]++;
    }
    walloc1d(&groupNode, groupNum, mem);
    for(i=(0);i<(groupNum);i++){
      walloc1d(&groupNode[i], groupSize[i], mem);
    }
    for(i=(0);i<(N);i++){
      groupNode[group[i]][groupind[i]] = i;
    }
    for(i=(0);i<(groupNum);i++){
      groupDepth[i] = -1;
    }
    groupUpNode[0] = -1;
    groupDepth[0] = 0;
    for(x=(0);x<(groupNum);x++){
      for(y=(0);y<(groupSize[x]);y++){
        i = groupNode[x][y];
        for(j=(0);j<(es[i]);j++){
          k = edge[i][j];
          if(x != group[k] && groupDepth[group[k]]==-1){
            groupUpNode[group[k]] = i;
            groupDepth[group[k]] = groupDepth[x] + 1;
          }
        }
      }
    }
  }
  int lca(int x, int y){
    int x1;
    int y1;
    int x2;
    int y2;
    x1 = group[x];
    x2 = groupind[x];
    y1 = group[y];
    y2 = groupind[y];
    while(groupDepth[x1] > groupDepth[y1]){
      x = groupUpNode[x1];
      x1 = group[x];
      x2 = groupind[x];
    }
    while(groupDepth[x1] < groupDepth[y1]){
      y = groupUpNode[y1];
      y1 = group[y];
      y2 = groupind[y];
    }
    while(x1 != y1){
      x = groupUpNode[x1];
      x1 = group[x];
      x2 = groupind[x];
      y = groupUpNode[y1];
      y1 = group[y];
      y2 = groupind[y];
    }
    if(x2 <= y2){
      return x;
    }
    return y;
  }
  int depth(int x){
    int x1;
    int x2;
    int res = 0;
    x1 = group[x];
    x2 = groupind[x];
    while(groupUpNode[x1] != -1){
      res += x2 + 1;
      x = groupUpNode[x1];
      x1 = group[x];
      x2 = groupind[x];
    }
    return res + x2;
  }
  int dist(int x, int y){
    int x1;
    int y1;
    int x2;
    int y2;
    int res = 0;
    x1 = group[x];
    x2 = groupind[x];
    y1 = group[y];
    y2 = groupind[y];
    while(groupDepth[x1] > groupDepth[y1]){
      res += x2 + 1;
      x = groupUpNode[x1];
      x1 = group[x];
      x2 = groupind[x];
    }
    while(groupDepth[x1] < groupDepth[y1]){
      res += y2 + 1;
      y = groupUpNode[y1];
      y1 = group[y];
      y2 = groupind[y];
    }
    while(x1 != y1){
      res += x2 + y2 + 2;
      x = groupUpNode[x1];
      x1 = group[x];
      x2 = groupind[x];
      y = groupUpNode[y1];
      y1 = group[y];
      y2 = groupind[y];
    }
    if(x2 <= y2){
      return res + y2 - x2;
    }
    return res + x2 - y2;
  }
  int up(int x){
    int x1 = group[x];
    int x2 = groupind[x];
    if(x2==0){
      return groupUpNode[x1];
    }
    return groupNode[x1][x2-1];
  }
  int up(int x, int d){
    int x1 = group[x];
    int x2 = groupind[x];
    while(d > x2){
      if(groupUpNode[x1]==-1){
        return -1;
      }
      d -= x2 + 1;
      x = groupUpNode[x1];
      x1 = group[x];
      x2 = groupind[x];
    }
    return groupNode[x1][x2-d];
  }
}
;
template<class T> struct HLD_segtree{
  HLD*hld;
  segtree<T>*seg;
  void init(HLD *hld__, T initval[], void **mem = &wmem){
    int i;
    int j;
    hld = hld__;
    walloc1d(&seg, hld->groupNum, mem);
    for(i=(0);i<(hld->groupNum);i++){
      seg[i].walloc(hld->groupSize[i], 0, mem);
      seg[i].setN(hld->groupSize[i], 0, 0);
      if(initval!=NULL){
        for(j=(0);j<(hld->groupSize[i]);j++){
          seg[i][j] = initval[ hld->groupNode[i][j] ];
        }
      }
      else{
        for(j=(0);j<(hld->groupSize[i]);j++){
          seg[i][j] = 0;
        }
      }
      seg[i].build();
    }
  }
  inline void change(int u, int v, T val){
    int ug;
    int vg;
    int ui;
    int vi;
    ug = hld->group[u];
    vg = hld->group[v];
    while(ug != vg){
      if(hld->groupDepth[ug] < hld->groupDepth[vg]){
        swap(u, v);
        swap(ug, vg);
      }
      seg[ug].change(0, hld->groupind[u]+1, val);
      u = hld->groupUpNode[ug];
      ug = hld->group[u];
    }
    ui = hld->groupind[u];
    vi = hld->groupind[v];
    seg[ug].change(min_L(ui, vi),max_L(ui, vi)+1, val);
  }
  inline void add(int u, int v, T val){
    int ug;
    int vg;
    int ui;
    int vi;
    ug = hld->group[u];
    vg = hld->group[v];
    while(ug != vg){
      if(hld->groupDepth[ug] < hld->groupDepth[vg]){
        swap(u, v);
        swap(ug, vg);
      }
      seg[ug].add(0, hld->groupind[u]+1, val);
      u = hld->groupUpNode[ug];
      ug = hld->group[u];
    }
    ui = hld->groupind[u];
    vi = hld->groupind[v];
    seg[ug].add(min_L(ui, vi),max_L(ui, vi)+1, val);
  }
  inline pair<T,int> getMin(int u, int v){
    pair<T,int> res;
    pair<T,int> tmp;
    int ug;
    int vg;
    int ui;
    int vi;
    ug = hld->group[u];
    vg = hld->group[v];
    res.first = numeric_limits<T>::max();
    res.second = -1;
    while(ug != vg){
      if(hld->groupDepth[ug] < hld->groupDepth[vg]){
        swap(u, v);
        swap(ug, vg);
      }
      tmp = seg[ug].getMin(0, hld->groupind[u]+1);
      tmp.second = hld->groupNode[ug][tmp.second];
      chmin(res, tmp);
      u = hld->groupUpNode[ug];
      ug = hld->group[u];
    }
    ui = hld->groupind[u];
    vi = hld->groupind[v];
    tmp = seg[ug].getMin(min_L(ui, vi),max_L(ui, vi)+1);
    tmp.second = hld->groupNode[ug][tmp.second];
    chmin(res, tmp);
    return res;
  }
  inline T getMinVal(int u, int v){
    return getMin(u,v).first;
  }
  inline int getMinInd(int u, int v){
    return getMin(u,v).second;
  }
  inline T getSum(int u, int v){
    T res;
    int ug;
    int vg;
    int ui;
    int vi;
    ug = hld->group[u];
    vg = hld->group[v];
    res = 0;
    while(ug != vg){
      if(hld->groupDepth[ug] < hld->groupDepth[vg]){
        swap(u, v);
        swap(ug, vg);
      }
      res += seg[ug].getSum(0, hld->groupind[u]+1);
      u = hld->groupUpNode[ug];
      ug = hld->group[u];
    }
    ui = hld->groupind[u];
    vi = hld->groupind[v];
    res += seg[ug].getSum(min_L(ui, vi),max_L(ui, vi)+1);
    return res;
  }
  inline void change_edge(int u, int v, T val){
    int x;
    int z;
    int d;
    z = hld->lca(u, v);
    d = hld->depth(z);
    if(z != u){
      x = hld->up(u, hld->depth(u) - d - 1);
      change(u, x, val);
    }
    if(z != v){
      x = hld->up(v, hld->depth(v) - d - 1);
      change(v, x, val);
    }
  }
  inline void add_edge(int u, int v, T val){
    int x;
    int z;
    int d;
    z = hld->lca(u, v);
    d = hld->depth(z);
    if(z != u){
      x = hld->up(u, hld->depth(u) - d - 1);
      add(u, x, val);
    }
    if(z != v){
      x = hld->up(v, hld->depth(v) - d - 1);
      add(v, x, val);
    }
  }
  inline pair<T,int> getMin_edge(int u, int v){
    int x;
    int z;
    int d;
    pair<T,int> res;
    pair<T,int> tmp;
    res.first = numeric_limits<T>::max();
    res.second = -1;
    z = hld->lca(u, v);
    d = hld->depth(z);
    if(z != u){
      x = hld->up(u, hld->depth(u) - d - 1);
      tmp = getMin(u, x);
      chmin(res, tmp);
    }
    if(z != v){
      x = hld->up(v, hld->depth(v) - d - 1);
      tmp = getMin(v, x);
      chmin(res, tmp);
    }
    return res;
  }
  inline T getMinVal_edge(int u, int v){
    return getMin_edge(u,v).first;
  }
  inline int getMinInd_edge(int u, int v){
    return getMin_edge(u,v).second;
  }
  inline T getSum_edge(int u, int v){
    int x;
    int z;
    int d;
    T res;
    res = 0;
    z = hld->lca(u, v);
    d = hld->depth(z);
    if(z != u){
      x = hld->up(u, hld->depth(u) - d - 1);
      res += getSum(u, x);
    }
    if(z != v){
      x = hld->up(v, hld->depth(v) - d - 1);
      res += getSum(v, x);
    }
    return res;
  }
}
;
int N;
int K;
int A[300000];
int B[300000];
int M[10];
int X[10][100000];
int U;
int V;
long long C[300000];
long long P[10];
wgraph<long long> g;
HLD hld;
HLD_segtree<long long> t;
long long di[10][100000+20];
long long db[10][10];
int main(){
  int aTqQ6rt8;
  wmem = memarr;
  int i;
  int j;
  int k;
  int m;
  void*mem;
  rd(N);
  rd(K);
  {
    int Lj4PdHRW;
    for(Lj4PdHRW=(0);Lj4PdHRW<(N-1);Lj4PdHRW++){
      rd(A[Lj4PdHRW]);A[Lj4PdHRW] += (-1);
      rd(B[Lj4PdHRW]);B[Lj4PdHRW] += (-1);
      rd(C[Lj4PdHRW]);
    }
  }
  for(i=(0);i<(K);i++){
    rd(M[i]);
    rd(P[i]);
    {
      int RZTsC2BF;
      for(RZTsC2BF=(0);RZTsC2BF<(M[i]);RZTsC2BF++){
        rd(X[i][RZTsC2BF]);X[i][RZTsC2BF] += (-1);
      }
    }
  }
  for(k=(0);k<(K);k++){
    m = N-1;
    for(i=(0);i<(M[k]);i++){
      arrInsert(m, m, A, N, B, X[k][i], C, 0LL);
    }
    mem = wmem;
    g.setEdge(N+1, m, A, B, C);
    g.getDist(N, di[k]);
    wmem = mem;
  }
  for(i=(0);i<(K);i++){
    for(j=(0);j<(K);j++){
      db[i][j] = 4611686016279904256LL;
    }
  }
  for(i=(0);i<(K);i++){
    db[i][i] = P[i];
  }
  for(i=(0);i<(K);i++){
    for(j=(0);j<(K);j++){
      for(k=(0);k<(M[j]);k++){
        chmin(db[i][j], di[i][X[j][k]] + P[i] + P[j]);
      }
    }
  }
  for(k=(0);k<(K);k++){
    for(i=(0);i<(K);i++){
      for(j=(0);j<(K);j++){
        chmin(db[i][j], db[i][k] + db[k][j] - P[k]);
      }
    }
  }
  g.setEdge(N, N-1, A, B, C);
  hld.init(g.g);
  t.init(&hld, NULL);
  for(i=(0);i<(N-1);i++){
    j = hld.depth(A[i]);
    k = hld.depth(B[i]);
    if(j > k){
      t.change(A[i], A[i], C[i]);
    }
    if(j < k){
      t.change(B[i], B[i], C[i]);
    }
  }
  int X9Iss0pP = rd_int();
  for(aTqQ6rt8=(0);aTqQ6rt8<(X9Iss0pP);aTqQ6rt8++){
    long long res = 4611686016279904256LL;
    rd(U);U += (-1);
    rd(V);V += (-1);
    chmin(res, t.getSum_edge(U, V));
    for(i=(0);i<(K);i++){
      for(j=(0);j<(K);j++){
        chmin(res, db[i][j] + di[i][U] + di[j][V]);
      }
    }
    wt_L(res);
    wt_L('\n');
  }
  return 0;
}
// cLay version 20210321-1 [beta]

// --- original code ---
// int N, K, A[3d5], B[3d5], M[10], X[10][1d5], U, V;
// ll C[3d5], P[10];
// wgraph<ll> g;
// HLD hld;
// HLD_segtree<ll> t;
// ll di[10][1d5+20], db[10][10];
// {
//   int i, j, k, m;
//   void *mem;
//   rd(N,K,(A--,B--,C)(N-1));
//   rep(i,K) rd(M[i], P[i], (X[i]--)(M[i]));
// 
//   rep(k,K){
//     m = N-1;
//     rep(i,M[k]) arrInsert(m, m, A, N, B, X[k][i], C, 0LL);
//     mem = wmem;
//     g.setEdge(N+1, m, A, B, C);
//     g.getDist(N, di[k]);
//     wmem = mem;
//   }
// 
//   rep(i,K) rep(j,K) db[i][j] = ll_inf;
//   rep(i,K) db[i][i] = P[i];
//   rep(i,K) rep(j,K) rep(k,M[j]) db[i][j] <?= di[i][X[j][k]] + P[i] + P[j];
//   rep(k,K) rep(i,K) rep(j,K) db[i][j] <?= db[i][k] + db[k][j] - P[k];
// 
//   g.setEdge(N, N-1, A, B, C);
//   hld.init(g.g);
//   t.init(&hld, NULL);
//   rep(i,N-1){
//     j = hld.depth(A[i]);
//     k = hld.depth(B[i]);
//     if(j > k) t.change(A[i], A[i], C[i]);
//     if(j < k) t.change(B[i], B[i], C[i]);
//   }
// 
//   REP(rd_int()){
//     ll res = ll_inf;
//     rd(U--, V--);
//     res <?= t.getSum_edge(U, V);
//     rep(i,K) rep(j,K) res <?= db[i][j] + di[i][U] + di[j][V];
//     wt(res);
//   }
// }