uniquepath

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 ≤ i ≤ Q-1) is represented as integers Ai,Bi,Ci and means the following:

  • If Ci=0: there was exactly one simple path (a path that never visits the same vertex twice) from Vertex Ai to Bi.
  • If Ci=1: there were two or more simple paths from Vertex Ai to Bi.

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 ≤ N ≤ 105
  • N-1 ≤ M ≤ N × (N-1)/2
  • 1 ≤ Q ≤ 105
  • 0 ≤ Ai,Bi ≤ N-1
  • Ai ≠ Bi
  • 0 ≤ Ci ≤ 1
  • All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M Q
A0 B0 C0
A1 B1 C1

.
.
.

AQ-1 BQ-1 CQ-1

Output

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

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

Submitting .cpp to 'uniquepath'


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Compile Errors


							
Time Limit: 1 Seconds
Memory Limit: 1024MB
No. of ACs: 9
Your best score: 0
Source: AGC38D

Subtask Score
1 100
2 0