Given an undirected graph with nodes labelled from \(1\) to \(N\), check whether or not node \(N\) can be reached from node \(1\).

Input Specification

The first line of the input will contain two integers \(N\) and \(M\) \((1 \le N, M \le 10^5)\), indicating the number of nodes and edges.

The next \(M\) lines will each contain two integers \(a_i\) and \(b_i\) \((1 \le a_i, b_i \le N)\), representing a bidirectional edge connecting the nodes \(a_i\) and \(b_i\).

Output Specification

Output YES if node \(N\) can be reached and NO otherwise.

Sample Input 1

5 4
1 4
4 3
3 1
2 5

Sample Output 1

NO

Sample Explanation 1

The following image shows the graph found in the sample input.

Sample Input 2

5 4
1 4
5 4
1 5
2 3

Sample Output 2

YES

Sample Explanation 2

The following image shows the graph found in the sample input. There are \(2\) possible paths from \(1\):

• 1 - 4 - 5
• 1 - 5