Problems
The smallest Topological Sort
The smallest Topological Sort
The directed unweighted graph is given. Find the lexicographically smallest topological ordering of its vertices.
Input data
The first line contains the number of vertices n~(1 \le n \le 10^5) and the number of edges m~(1 \le m \le 10^5) in a graph. Each of the next m lines describes the edge of the graph — two numbers, the initial and final vertex.
Output data
Print the lexicographically smallest topological ordering of graph's vertices. If its impossible to sort graph topologically, print -1.
Examples
Input example #1
6 6 1 2 3 2 4 2 2 5 6 5 4 6
Output example #1
1 3 4 2 6 5