Envy

For a connected undirected weighted graph G, MST (minimum spanning tree) is a subgraph of G that contains all of G‘s vertices, is a tree, and sum of its edges is minimum possible.

You are given a graph G. If you run a MST algorithm on graph it would give you only one MST and it causes other edges to become jealous. You are given some queries, each query contains a set of edges of graph G, and you should determine whether there is a MST containing all these edges or not.

Input

The first line contains two integers n, m (2  ≤ n, m  ≤ 5·10⁵, n - 1 ≤ m) — the number of vertices and edges in the graph and the number of queries.

The i-th of the next m lines contains three integers u _i, v _i, w _i ( u _i ≠ v _i, 1 ≤ w _i ≤ 5·10⁵) — the endpoints and weight of the i-th edge. There can be more than one edges between two vertices. It’s guaranteed that the given graph is connected.

The next line contains a single integer q (1 ≤ q ≤ 5·10⁵) — the number of queries.

q lines follow, the i-th of them contains the i-th query. It starts with an integer k _i (1 ≤ k _i ≤ n - 1) — the size of edges subset and continues with k _i distinct space-separated integers from 1 to m — the indices of the edges. It is guaranteed that the sum of k _i for 1 ≤ i ≤ q does not exceed 5·10⁵.

Output

For each query you should print “YES” (without quotes) if there’s a MST containing these edges and “NO” (of course without quotes again) otherwise.

Example

input

5 7
1 2 2
1 3 2
2 3 1
2 4 1
3 4 1
3 5 2
4 5 2
4
2 3 4
3 3 4 5
2 1 7
2 1 2

output

YES
NO
YES
NO

Note

This is the graph of sample:

Weight of minimum spanning tree on this graph is 6.

MST with edges (1, 3, 4, 6), contains all of edges from the first query, so answer on the first query is “YES”.

Edges from the second query form a cycle of length 3, so there is no spanning tree including these three edges. Thus, answer is “NO”.

Solution:

#include <bits/stdc++.h>

using namespace std;

class node {
public:
int id;
node* l;
node* r;
node* p;
bool rev;
int sz;
// declare extra variables:

node(int _id) {
id = _id;
l = r = p = NULL;
rev = false;
sz = 1;
// init extra variables:

}

void unsafe_reverse() {
rev ^= 1;
swap(l, r);
pull();
}

// apply changes:
void unsafe_apply() {

}

void push() {
if (rev) {
if (l != NULL) {
l->unsafe_reverse();
}
if (r != NULL) {
r->unsafe_reverse();
}
rev = 0;
}
// now push everything else:

}

void pull() {
sz = 1;
// now init from self:

if (l != NULL) {
l->p = this;
sz += l->sz;
// now pull from l:

}
if (r != NULL) {
r->p = this;
sz += r->sz;
// now pull from r:

}
}
};

namespace splay_tree {
bool is_bst_root(node* v) {
if (v == NULL) {
return false;
}
return (v->p == NULL || (v->p->l != v && v->p->r != v));
}

void rotate(node* v) {
node* u = v->p;
assert(u != NULL);
u->push();
v->push();
if (v == u->l) {
u->l = v->r;
v->r = u;
} else {
u->r = v->l;
v->l = u;
}
v->p = u->p;
if (v->p != NULL) {
if (v->p->l == u) {
v->p->l = v;
}
if (v->p->r == u) {
v->p->r = v;
}
}
u->pull();
v->pull();
}

void splay(node* v) {
if (v == NULL) {
return;
}
while (!is_bst_root(v)) {
node* u = v->p;
if (!is_bst_root(u)) {
if ((u->l == v) ^ (u->p->l == u)) {
rotate(v);
} else {
rotate(u);
}
}
rotate(v);
}
}

pair<node*,int> find(node* v, const function<int(node*)> &go_to) {
// go_to returns: 0 -- found; -1 -- go left; 1 -- go right
if (v == NULL) {
return {NULL, 0};
}
splay(v);
int dir;
while (true) {
v->push();
dir = go_to(v);
if (dir == 0) {
break;
}
node* u = (dir == -1 ? v->l : v->r);
if (u == NULL) {
break;
}
v = u;
}
splay(v);
return {v, dir};
}

node* get_leftmost(node* v) {
return find(v, [&](node*) { return -1; }).first;
}

node* get_rightmost(node* v) {
return find(v, [&](node*) { return 1; }).first;
}

node* get_kth(node* v, int k) { // 0-indexed
pair<node*,int> p = find(v, [&](node* u) {
if (u->l != NULL) {
if (u->sz > k) {
return -1;
}
k -= u->sz;
}
if (k == 0) {
return 0;
}
k--;
return 1;
});
return (p.second == 0 ? p.first : NULL);
}

int get_position(node* v) { // 0-indexed
splay(v);
return (v->l != NULL ? v->sz : 0);
}

node* get_bst_root(node* v) {
splay(v);
return v;
}

pair<node*,node*> split(node* v, const function<bool(node*)> &is_right) {
if (v == NULL) {
return {NULL, NULL};
}
pair<node*,int> p = find(v, [&](node* u) { return is_right(u) ? -1 : 1; });
v = p.first;
v->push();
if (p.second == -1) {
node* u = v->l;
if (u == NULL) {
return {NULL, v};
}
v->l = NULL;
u->p = v->p;
u = get_rightmost(u);
v->p = u;
v->pull();
return {u, v};
} else {
node* u = v->r;
if (u == NULL) {
return {v, NULL};
}
v->r = NULL;
v->pull();
return {v, u};
}
}

pair<node*,node*> split_leftmost_k(node* v, int k) {
return split(v, [&](node* u) {
int left_and_me = (u->l != NULL ? u->l->sz : 0) + 1;
if (k >= left_and_me) {
k -= left_and_me;
return false;
}
return true;
});
}

node* merge(node* v, node* u) {
if (v == NULL) {
return u;
}
if (u == NULL) {
return v;
}
v = get_rightmost(v);
assert(v->r == NULL);
splay(u);
v->push();
v->r = u;
v->pull();
return v;
}

node* remove(node* v) {
splay(v);
v->push();
node* x = v->l;
node* y = v->r;
v->l = v->r = NULL;
node* z = merge(x, y);
z->p = v->p;
v->p = NULL;
return z;
}

int get_size(node* v) {
splay(v);
return v->sz;
}

template<typename... T>
void apply(node* v, T... args) {
splay(v);
v->unsafe_apply(args...);
}

void reverse(node* v) {
splay(v);
v->unsafe_reverse();
}
}

using namespace splay_tree;

template<bool rooted>
class link_cut_tree {
public:
int n;
vector<node*> nodes;

link_cut_tree(int _n) : n(_n) {
nodes.resize(n);
for (int i = 0; i < n; i++) {
      nodes[i] = new node(i);
    }
  }

  int add_node() {
    int id = (int) nodes.size();
    nodes.push_back(new node(id));
    return id;
  }

  void expose(node* v) {
    node* r = NULL;
    node* u = v;
    while (u != NULL) {
      splay(u);
      u->push();
u->r = r;
u->pull();
r = u;
u = u->p;
}
splay(v);
assert(v->p == NULL);
}

int get_root(int i) {
node* v = nodes[i];
expose(v);
return get_leftmost(v)->id;
}

bool link(int i, int j) { // for rooted: (x, parent[x])
if (i == j) {
return false;
}
node* v = nodes[i];
node* u = nodes[j];
if (rooted) {
splay(v);
assert(v->p == NULL && v->l == NULL); // must be a root
} else {
make_root(i);
}
expose(u);
if (v->p != NULL) {
return false;
}
v->p = u;
return true;
}

bool cut(int i, int j) { // for rooted: (x, parent[x])
if (i == j) {
return false;
}
node* v = nodes[i];
node* u = nodes[j];
expose(u);
splay(v);
if (v->p != u) {
if (rooted) {
return false;
}
swap(u, v);
expose(u);
splay(v);
if (v->p != u) {
return false;
}
}
v->p = NULL;
return true;
}

bool connected(int i, int j) {
if (i == j) {
return true;
}
node* v = nodes[i];
node* u = nodes[j];
expose(v);
assert(v->p == NULL);
expose(u);
return v->p != NULL;
}

int lca(int i, int j) {
if (i == j) {
return i;
}
node* v = nodes[i];
node* u = nodes[j];
expose(v);
assert(v->p == NULL);
expose(u);
if (v->p == NULL) {
return -1;
}
splay(v);
if (v->p == NULL) {
return v->id;
}
return v->p->id;
}

bool is_ancestor(int i, int j) {
if (i == j) {
return true;
}
node* v = nodes[i];
node* u = nodes[j];
expose(u);
assert(u->p == NULL);
splay(v);
return v->p == NULL && u->p != NULL;
}

void make_root(int i) {
assert(!rooted);
node* v = nodes[i];
expose(v);
assert(v->r == NULL);
reverse(v);
}

node* get_path_from_root(int i) {
node* v = nodes[i];
expose(v);
return v;
}

template<typename... T>
void apply(int i, T... args) {
node* v = nodes[i];
splay_tree::apply(v, args...);
}
};

int main() {
ios::sync_with_stdio(false);
cin.tie(0);
int n, m;
cin >> n >> m;
const int MAX = 500010;
vector<vector<int>> g(MAX);
vector<map<int,vector<int>>> t(MAX);
vector<int> from(m), to(m), cost(m);
for (int i = 0; i < m; i++) {
    cin >> from[i] >> to[i] >> cost[i];
from[i]--; to[i]--;
g[cost[i]].push_back(i);
}
int tt;
cin >> tt;
for (int qq = 0; qq < tt; qq++) {
    int foo;
    cin >> foo;
for (int i = 0; i < foo; i++) {
      int bar;
      cin >> bar;
bar--;
t[cost[bar]][qq].push_back(bar);
}
}
vector<int> res(tt, 1);
link_cut_tree<false> lct(n);
vector<int> to_cut;
for (int i = 0; i < MAX; i++) {
    for (auto &p : t[i]) {
      to_cut.clear();
      for (int j : p.second) {
        if (lct.connected(from[j], to[j])) {
          res[p.first] = 0;
          break;
        } else {
          lct.link(from[j], to[j]);
          to_cut.push_back(j);
        }
      }
      for (int j : to_cut) {
        lct.cut(from[j], to[j]);
      }
    }
    for (int j : g[i]) {
      lct.link(from[j], to[j]);
    }
  }
  for (int i = 0; i < tt; i++) {
    cout << (res[i] ? "YES" : "NO") << '\n';
  }
  return 0;
}