Problem Statement

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.

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.

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.

Sample Input 1

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

Sample Output 1

Yes

For example, consider a graph with edges (0,1),(1,2),(1,4),(2,3),(2,4). This graph matches the clues.

Sample Input 2

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

Sample Output 2

No

Sample Input 3

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

Sample Output 3

No

见题面 Input 部分

见题面 Output 部分