#include<bits/stdc++.h>
#define ll long long
#define ljc 998244353
using namespace std;
#define gc getchar
inline ll read(){
    register ll x=0,f=1;char ch=gc();
    while (!isdigit(ch)){if (ch=='-') f=-1;ch=gc();}
    while (isdigit(ch)){x=(x<<3)+(x<<1)+ch-'0';ch=gc();}
    return (f==1)?x:-x;
}
ll n,m,Q,F[1010101],sz[1010101]; 
struct node{
	int id,x,y;
}q[1010101];
inline bool cmp(node a,node b){
	return a.id<b.id;
}
int find(int u){
	if (F[u]!=u) F[u]=find(F[u]);
	return F[u];
}
inline void fail(){
	puts("No");exit(0);
}
signed main(){
	n=read(),m=read(),Q=read();
	for (int i=1;i<=n;i++) F[i]=i,sz[i]=1;
	for (int i=1;i<=Q;i++){
		q[i].x=read()+1,q[i].y=read()+1,q[i].id=read();
	}
	sort(q+1,q+1+Q,cmp);
	register int i;
	ll tot=0,_min=0,_max=0,tot1=0;
	for (i=1;i<=Q;i++){
		if (q[i].id==1) break;
		int xx=find(q[i].x),yy=find(q[i].y);
		if (xx==yy) continue;
		F[xx]=yy,tot1++;
		sz[yy]+=sz[xx];
	}
	bool flag=0;
	if (i==Q+1) flag=1;
	for (;i<=Q;i++){
		if (find(q[i].x)==find(q[i].y)) fail();
	}
	for (int i=1;i<=n;i++){
		if (sz[find(i)]==1) tot++;
	}
	ll xx=(n-tot-tot1);
	if (xx==1&&tot==1&&!flag) fail();
	_min=(flag==1?n-1:n);
	_max=tot1+(xx+tot)*(xx+tot-1)/2;
	if (m>=_min&&m<=_max){
		puts("Yes");
		return 0;
	}
	fail();
	return 0;
}


### Prompt

In Cpp, your task is to solve 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 ll long long
#define ljc 998244353
using namespace std;
#define gc getchar
inline ll read(){
    register ll x=0,f=1;char ch=gc();
    while (!isdigit(ch)){if (ch=='-') f=-1;ch=gc();}
    while (isdigit(ch)){x=(x<<3)+(x<<1)+ch-'0';ch=gc();}
    return (f==1)?x:-x;
}
ll n,m,Q,F[1010101],sz[1010101]; 
struct node{
	int id,x,y;
}q[1010101];
inline bool cmp(node a,node b){
	return a.id<b.id;
}
int find(int u){
	if (F[u]!=u) F[u]=find(F[u]);
	return F[u];
}
inline void fail(){
	puts("No");exit(0);
}
signed main(){
	n=read(),m=read(),Q=read();
	for (int i=1;i<=n;i++) F[i]=i,sz[i]=1;
	for (int i=1;i<=Q;i++){
		q[i].x=read()+1,q[i].y=read()+1,q[i].id=read();
	}
	sort(q+1,q+1+Q,cmp);
	register int i;
	ll tot=0,_min=0,_max=0,tot1=0;
	for (i=1;i<=Q;i++){
		if (q[i].id==1) break;
		int xx=find(q[i].x),yy=find(q[i].y);
		if (xx==yy) continue;
		F[xx]=yy,tot1++;
		sz[yy]+=sz[xx];
	}
	bool flag=0;
	if (i==Q+1) flag=1;
	for (;i<=Q;i++){
		if (find(q[i].x)==find(q[i].y)) fail();
	}
	for (int i=1;i<=n;i++){
		if (sz[find(i)]==1) tot++;
	}
	ll xx=(n-tot-tot1);
	if (xx==1&&tot==1&&!flag) fail();
	_min=(flag==1?n-1:n);
	_max=tot1+(xx+tot)*(xx+tot-1)/2;
	if (m>=_min&&m<=_max){
		puts("Yes");
		return 0;
	}
	fail();
	return 0;
}


```