#include <iostream>
#include <vector>
#include <cstdio>
#include <sstream>
#include <map>
#include <string>
#include <algorithm>
#include <queue>
#include <cmath>
#include <functional>
#include <set>
#include <ctime>
#include <random>
#include <chrono>
#include <cassert>
#include <tuple>
#include <utility>
using namespace std;

namespace {
  using Integer = long long; //__int128;
  template<class T, class S> istream& operator >> (istream& is, pair<T,S>& p){return is >> p.first >> p.second;}
  template<class T> istream& operator >> (istream& is, vector<T>& vec){for(T& val: vec) is >> val; return is;}
  template<class T> istream& operator ,  (istream& is, T& val){ return is >> val;}
  template<class T, class S> ostream& operator << (ostream& os, const pair<T,S>& p){return os << p.first << " " << p.second;}
  template<class T> ostream& operator << (ostream& os, const vector<T>& vec){for(size_t i=0; i<vec.size(); i++) os << vec[i] << (i==vec.size()-1?"":" "); return os;}
  template<class T> ostream& operator ,  (ostream& os, const T& val){ return os << " " << val;}

  template<class H> void print(const H& head){ cout << head; }
  template<class H, class ... T> void print(const H& head, const T& ... tail){ cout << head << " "; print(tail...); }
  template<class ... T> void println(const T& ... values){ print(values...); cout << endl; }

  template<class H> void eprint(const H& head){ cerr << head; }
  template<class H, class ... T> void eprint(const H& head, const T& ... tail){ cerr << head << " "; eprint(tail...); }
  template<class ... T> void eprintln(const T& ... values){ eprint(values...); cerr << endl; }

  class range{ Integer start_, end_, step_; public: struct range_iterator{ Integer val, step_; range_iterator(Integer v, Integer step) : val(v), step_(step) {} Integer operator * (){return val;} void operator ++ (){val += step_;} bool operator != (range_iterator& x){return step_ > 0 ? val < x.val : val > x.val;} }; range(Integer len) : start_(0), end_(len), step_(1) {} range(Integer start, Integer end) : start_(start), end_(end), step_(1) {} range(Integer start, Integer end, Integer step) : start_(start), end_(end), step_(step) {} range_iterator begin(){ return range_iterator(start_, step_); } range_iterator   end(){ return range_iterator(  end_, step_); } };

  inline string operator "" _s (const char* str, size_t size){ return move(string(str)); }
  constexpr Integer my_pow(Integer x, Integer k, Integer z=1){return k==0 ? z : k==1 ? z*x : (k&1) ? my_pow(x*x,k>>1,z*x) : my_pow(x*x,k>>1,z);}
  constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z=1){return k==0 ? z%M : k==1 ? z*x%M : (k&1) ? my_pow_mod(x*x%M,k>>1,M,z*x%M) : my_pow_mod(x*x%M,k>>1,M,z);}
  constexpr unsigned long long operator "" _ten (unsigned long long value){ return my_pow(10,value); }

  inline int k_bit(Integer x, int k){return (x>>k)&1;} //0-indexed

  mt19937 mt(chrono::duration_cast<chrono::nanoseconds>(chrono::steady_clock::now().time_since_epoch()).count());

  template<class T> string join(const vector<T>& v, const string& sep){ stringstream ss; for(size_t i=0; i<v.size(); i++){ if(i>0) ss << sep; ss << v[i]; } return ss.str(); }

  inline string operator * (string s, int k){ string ret; while(k){ if(k&1) ret += s; s += s; k >>= 1; } return ret; }
}
constexpr long long mod = 9_ten + 7;


class UnionFindTree{
  struct base_node{
    int parent;
    int rank;
    int size;
  };
  
  vector<base_node> node;
 public:
  UnionFindTree(int n){
    node.resize(n);
    for(int i=0; i<n; i++){
      node[i].parent=i;
      node[i].rank=0;
      node[i].size=1;
    }
  }

  int find(int x){  //return root node of x
    if(node[x].parent == x) return x;
    else{
      return node[x].parent = find(node[x].parent);
    }
  }
  
  bool same(int x, int y){
    return find(x) == find(y);
  }

  int size(int at){
    return node[find(at)].size;
  }

  void unite(int x, int y){
    x = find(node[x].parent);
    y = find(node[y].parent);

    if(x==y) return;

    if(node[x].rank < node[y].rank){
      node[x].parent = y;
      node[y].size += node[x].size;
    }else if(node[x].rank > node[y].rank){
      node[y].parent = x;
      node[x].size += node[y].size;
    }else{
      node[x].rank++;
      unite(x,y);
    }
  }
};


int main(){
  long long n, m, q;
  cin >> n, m, q;

  vector<pair<int, int>> q0, q1;
  for(int i=0; i<q; i++){
    long long a, b, c;
    cin >> a, b, c;
    if(c == 0){
      q0.emplace_back(a, b);
    }else{
      q1.emplace_back(a, b);
    }
  }

  UnionFindTree uft(n);
  for(auto e: q0){
    uft.unite(e.first, e.second);
  }

  set<int> d;
  bool ok = true;
  for(auto e: q1){
    int a,b;
    tie(a,b) = e;
    if(uft.same(a,b)){
      ok = false;
    }
    d.insert(uft.find(a));
    d.insert(uft.find(b));
  }

  set<int> v;
  for(int i=0; i<n; i++){
    v.insert(uft.find(i));
  }

  long long s = v.size();

  if(ok){
    if(q1.size() == 0){
      long long base = (n-1)-(s-1);
      long long e_min = base + (s-1);
      long long e_max = base + (s * (s-1)) / 2;

      ok = e_min <= m && m <= e_max;
    } else {
      long long base = (n-1)-(s-1);
      long long e_min = base + s;
      long long e_max = base + (s * (s-1)) / 2;

      ok = e_min <= m && m <= e_max;
    }
  }

  println(ok ? "Yes" : "No");

  return 0;
}


Measured memory_bytes: 11636