Problem Description

Find the lexicographically smallest Eulerian path in a directed graph.

Input Format

The first line contains two integers \( n \) and \( m \), representing the number of vertices and edges in the directed graph, respectively.

The next \( m \) lines each contain two integers \( u \) and \( v \), indicating that there is a directed edge from \( u \) to \( v \).

Output Format

If no Eulerian path exists, output a single line containing No.

Otherwise, output a single line with \( m+1 \) numbers, representing the lexicographically smallest Eulerian path.

Sample Input and Output

Sample Input #1

4 6
1 3
2 1
4 2
3 3
1 2
3 4

Sample Output #1

1 2 1 3 3 4 2

Sample Input #2

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

Sample Output #2

1 2 3 4 3 5

Sample Input #3

4 3
1 2
1 3
1 4

Sample Output #3

No

Notes

For 50% of the test cases, \( n, m \leq 10^3 \).

For 100% of the test cases, \( 1 \leq u, v \leq n \leq 10^5 \), \( m \leq 2 \times 10^5 \).

The graph is guaranteed to be connected when the directed edges are considered as undirected edges.

Data Generator

见题面 Input 部分

见题面 Output 部分