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题目描述

This is a problem given in the Graduate Entrance Exam in 2023: Given a directed graph G, you are supposed to tell if there exists a unique topological order of its vertices.

输入格式

Each input file contains one test case. For each case, the first line gives two positive integers $n$ ($\le 10^4$), the number of vertices in the graph, and $m$ ($\le 10^5$), the number of directed edges. Then $m$ lines follow, each gives the start and the end vertices of an edge. The vertices are numbered from 1 to $n$. It is guaranteed that no duplicated edge is given.

输出格式

Output the vertices with the smallest in-degree in the first line, in ascending order. Then if there exists a unique topological order of all the vertices, first print in a line Yes and then output the topological sequence in the next line. Or if the answer is no, just print in a line No. All the numbers in a line must be separated by exactly 1 space, and there must be no extra space at the beginning or the end of the line.

样例

6 9
2 1
1 3
5 2
5 4
2 3
2 6
3 4
6 4
6 1

5
Yes
5 2 6 1 3 4

6 8
1 2
1 3
5 2
5 4
2 3
2 6
3 4
6 4

1 5
No

限制

对于所有的测试用例,限制为150 ms, 64 MB