#include<bits/stdc++.h>
#define rep(i,a,b) for(int i=(a);i<=(b);i++)
#define per(i,a,b) for(int i=(a);i>=(b);i--)
#define REP(i,n) for(int i=(0);i<(n);i++)
#define fi first
#define se second
#define pb push_back
#define mp make_pair
using namespace std;
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef long long ll;

template<class T> inline void read(T &x){
	int f=0;x=0;char ch=getchar();
	for(;!isdigit(ch);ch=getchar())f|=(ch=='-');
	for(;isdigit(ch);ch=getchar())x=x*10+ch-'0';
	if(f)x=-x;
}

const int N=100005;
int pa[N],a[N],b[N],c[N],n,Q,c1,sz;
ll m;

int getpa(int x){
	return pa[x]==x?x:pa[x]=getpa(pa[x]);
}

int main(){
	read(n),read(m),read(Q);
	rep(i,1,n)pa[i]=i;
	rep(i,1,Q){
		read(a[i]),read(b[i]),read(c[i]);
		a[i]++,b[i]++;
		if(c[i])c1++;
		else pa[getpa(a[i])]=getpa(b[i]);
	}
	rep(i,1,Q)
		if(c[i]&&getpa(a[i])==getpa(b[i])){
			puts("No");
			return 0;
		}
	if(m==n-1&&c1){
		puts("No");
		return 0;
	}
	rep(i,1,n)if(pa[i]==i)++sz;
	if(sz==2){
		puts(m==n-1&&!c1?"Yes":"No");
		return 0;
	}
	if(m<=n+(ll)sz*(sz-3)/2)puts("Yes");
	else puts("No");
	return 0;
}

### Prompt

Construct a cpp code solution to the problem outlined:

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 rep(i,a,b) for(int i=(a);i<=(b);i++)
#define per(i,a,b) for(int i=(a);i>=(b);i--)
#define REP(i,n) for(int i=(0);i<(n);i++)
#define fi first
#define se second
#define pb push_back
#define mp make_pair
using namespace std;
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef long long ll;

template<class T> inline void read(T &x){
	int f=0;x=0;char ch=getchar();
	for(;!isdigit(ch);ch=getchar())f|=(ch=='-');
	for(;isdigit(ch);ch=getchar())x=x*10+ch-'0';
	if(f)x=-x;
}

const int N=100005;
int pa[N],a[N],b[N],c[N],n,Q,c1,sz;
ll m;

int getpa(int x){
	return pa[x]==x?x:pa[x]=getpa(pa[x]);
}

int main(){
	read(n),read(m),read(Q);
	rep(i,1,n)pa[i]=i;
	rep(i,1,Q){
		read(a[i]),read(b[i]),read(c[i]);
		a[i]++,b[i]++;
		if(c[i])c1++;
		else pa[getpa(a[i])]=getpa(b[i]);
	}
	rep(i,1,Q)
		if(c[i]&&getpa(a[i])==getpa(b[i])){
			puts("No");
			return 0;
		}
	if(m==n-1&&c1){
		puts("No");
		return 0;
	}
	rep(i,1,n)if(pa[i]==i)++sz;
	if(sz==2){
		puts(m==n-1&&!c1?"Yes":"No");
		return 0;
	}
	if(m<=n+(ll)sz*(sz-3)/2)puts("Yes");
	else puts("No");
	return 0;
}

```