Score : $300$ points

Problem Statement

You are given a simple undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1, 2, \dots, N$, and the edges are numbered $1, 2, \dots, M$. Edge $i \, (i = 1, 2, \dots, M)$ connects vertices $u_i$ and $v_i$.

Determine if this graph is a path graph.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $0 \leq M \leq 2 \times 10^5$
• $1 \leq u_i, v_i \leq N \, (i = 1, 2, \dots, M)$
• All values in the input are integers.
• The graph given in the input is simple.

Input

The input is given from Standard Input in the following format:

$N$ $M$

$u_1$ $v_1$

$u_2$ $v_2$

$\vdots$

$u_M$ $v_M$

Output

Print Yes if the given graph is a path graph; print No otherwise.

4 3
1 3
4 2
3 2

Yes

Illustrated below is the given graph, which is a path graph.

2 0

No

Illustrated below is the given graph, which is not a path graph.

5 5
1 2
2 3
3 4
4 5
5 1

No

Illustrated below is the given graph, which is not a path graph.