#include <bits/stdc++.h>
#define syosu(x) fixed<<setprecision(x)
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> P;
typedef pair<double,double> pdd;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<string> vs;
typedef vector<P> vp;
typedef vector<vp> vvp;
typedef vector<pll> vpll;
typedef pair<int,P> pip;
typedef vector<pip> vip;
const int inf=1<<30;
const ll INF=1ll<<55;
const double pi=acos(-1);
const double eps=1e-8;
const ll mod=1e9+7;
const int dx[4]={-1,0,1,0},dy[4]={0,-1,0,1};

int n,q;
ll m;
vvi g;
vi b;
vp a;

void dfs(int v,int t){
	b[v]=t;
	for(auto u:g[v]) if(b[u]<0) dfs(u,t);
}

int main(){
	cin>>n>>m>>q;
	b=vi(n,-1);
	g=vvi(n);
	for(int i=0;i<q;i++){
		int t,u,v;
		cin>>u>>v>>t;
		if(t==0){
			g[u].push_back(v);
			g[v].push_back(u);
		}
		else a.push_back({u,v});
	}
	ll t=0;
	bool res=1;
	for(int i=0;i<n;i++) if(b[i]<0) dfs(i,t++);
	for(auto p:a) if(b[p.first]==b[p.second]) res=0;
	t=t*(t-1)/2+n-t;
	if(t<m) res=0;
	if(!a.empty()&&m==n-1) res=0; 
	cout<<(res?"Yes":"No")<<endl;
}
### Prompt

Please create a solution in CPP to the following problem:

Snuke's mother gave Snuke an undirected graph consisting of N vertices numbered 0 to N-1 and M edges. This graph was connected and contained no parallel edges or self-loops.

One day, Snuke broke this graph. Fortunately, he remembered Q clues about the graph. The i-th clue (0 \leq i \leq Q-1) is represented as integers A_i,B_i,C_i and means the following:

* If C_i=0: there was exactly one simple path (a path that never visits the same vertex twice) from Vertex A_i to B_i.
* If C_i=1: there were two or more simple paths from Vertex A_i to B_i.



Snuke is not sure if his memory is correct, and worried whether there is a graph that matches these Q clues. Determine if there exists a graph that matches Snuke's memory.

Constraints

* 2 \leq N \leq 10^5
* N-1 \leq M \leq N \times (N-1)/2
* 1 \leq Q \leq 10^5
* 0 \leq A_i,B_i \leq N-1
* A_i \neq B_i
* 0 \leq C_i \leq 1
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N M Q
A_0 B_0 C_0
A_1 B_1 C_1
\vdots
A_{Q-1} B_{Q-1} C_{Q-1}


Output

If there exists a graph that matches Snuke's memory, print `Yes`; otherwise, print `No`.

Examples

Input

5 5 3
0 1 0
1 2 1
2 3 0


Output

Yes


Input

4 4 3
0 1 0
1 2 1
2 3 0


Output

No


Input

10 9 9
7 6 0
4 5 1
9 7 0
2 9 0
2 3 0
4 1 0
8 0 0
9 1 0
3 0 0


Output

No

### Response

```cpp
#include <bits/stdc++.h>
#define syosu(x) fixed<<setprecision(x)
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> P;
typedef pair<double,double> pdd;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<string> vs;
typedef vector<P> vp;
typedef vector<vp> vvp;
typedef vector<pll> vpll;
typedef pair<int,P> pip;
typedef vector<pip> vip;
const int inf=1<<30;
const ll INF=1ll<<55;
const double pi=acos(-1);
const double eps=1e-8;
const ll mod=1e9+7;
const int dx[4]={-1,0,1,0},dy[4]={0,-1,0,1};

int n,q;
ll m;
vvi g;
vi b;
vp a;

void dfs(int v,int t){
	b[v]=t;
	for(auto u:g[v]) if(b[u]<0) dfs(u,t);
}

int main(){
	cin>>n>>m>>q;
	b=vi(n,-1);
	g=vvi(n);
	for(int i=0;i<q;i++){
		int t,u,v;
		cin>>u>>v>>t;
		if(t==0){
			g[u].push_back(v);
			g[v].push_back(u);
		}
		else a.push_back({u,v});
	}
	ll t=0;
	bool res=1;
	for(int i=0;i<n;i++) if(b[i]<0) dfs(i,t++);
	for(auto p:a) if(b[p.first]==b[p.second]) res=0;
	t=t*(t-1)/2+n-t;
	if(t<m) res=0;
	if(!a.empty()&&m==n-1) res=0; 
	cout<<(res?"Yes":"No")<<endl;
}
```