#include<bits/stdc++.h>
using namespace std;

#define int long long 

void read(int &x) {
    x=0;int f=1;char ch=getchar();
    for(;!isdigit(ch);ch=getchar()) if(ch=='-') f=-f;
    for(;isdigit(ch);ch=getchar()) x=x*10+ch-'0';x*=f;
}

void print(int x) {
    if(x<0) putchar('-'),x=-x;
    if(!x) return ;print(x/10),putchar(x%10+48);
}
void write(int x) {if(!x) putchar('0');else print(x);putchar('\n');}

#define lf double
#define ll long long 

#define pii pair<int,int >
#define vec vector<int >

#define pb push_back
#define mp make_pair
#define fr first
#define sc second

#define FOR(i,l,r) for(int i=l,i##_r=r;i<=i##_r;i++)

const int maxn = 1e6+10;
const int inf = 1e9;
const lf eps = 1e-8;
const int mod = 1e9+7;

int fa[maxn],n,m,t;
vector<pii > a;

int find(int x) {return fa[x]==x?x:fa[x]=find(fa[x]);}

signed main() {
    read(n),read(m),read(t);int c=0;
    for(int i=1;i<=n;i++) fa[i]=i;
    for(int i=1;i<=t;i++) {
        int x,y,z;read(x),read(y),read(z);
        if(z) a.pb(mp(x,y));
        else {
            x=find(x),y=find(y);
            if(x!=y) fa[x]=y,c++;
        }
    }c=n-c;
    for(auto x:a) if(find(x.fr)==find(x.sc)) return puts("No"),0;
    int l=a.size()?max(3ll,c):c-1,r=c*(c-1)/2;
    if(m-n+c>=l&&m-n+c<=r) puts("Yes");
    else puts("No");
    return 0;
}

### Prompt

Create a solution in Cpp for 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>
using namespace std;

#define int long long 

void read(int &x) {
    x=0;int f=1;char ch=getchar();
    for(;!isdigit(ch);ch=getchar()) if(ch=='-') f=-f;
    for(;isdigit(ch);ch=getchar()) x=x*10+ch-'0';x*=f;
}

void print(int x) {
    if(x<0) putchar('-'),x=-x;
    if(!x) return ;print(x/10),putchar(x%10+48);
}
void write(int x) {if(!x) putchar('0');else print(x);putchar('\n');}

#define lf double
#define ll long long 

#define pii pair<int,int >
#define vec vector<int >

#define pb push_back
#define mp make_pair
#define fr first
#define sc second

#define FOR(i,l,r) for(int i=l,i##_r=r;i<=i##_r;i++)

const int maxn = 1e6+10;
const int inf = 1e9;
const lf eps = 1e-8;
const int mod = 1e9+7;

int fa[maxn],n,m,t;
vector<pii > a;

int find(int x) {return fa[x]==x?x:fa[x]=find(fa[x]);}

signed main() {
    read(n),read(m),read(t);int c=0;
    for(int i=1;i<=n;i++) fa[i]=i;
    for(int i=1;i<=t;i++) {
        int x,y,z;read(x),read(y),read(z);
        if(z) a.pb(mp(x,y));
        else {
            x=find(x),y=find(y);
            if(x!=y) fa[x]=y,c++;
        }
    }c=n-c;
    for(auto x:a) if(find(x.fr)==find(x.sc)) return puts("No"),0;
    int l=a.size()?max(3ll,c):c-1,r=c*(c-1)/2;
    if(m-n+c>=l&&m-n+c<=r) puts("Yes");
    else puts("No");
    return 0;
}

```