Score : $400$ points

问题描述

在满足以下条件的序列 $P$ 中，找出字典序最小的序列。这些序列是对 $(1, 2, \dots, N)$ 的排列。

• 对于每个 $i = 1, \dots, M$，在序列 $P$ 中，$A_i$ 出现的位置早于 $B_i$。

如果不存在这样的序列 $P$，则输出 -1。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Among the sequences $P$ that are permutations of $(1, 2, \dots, N)$ and satisfy the condition below, find the lexicographically smallest sequence.

• For each $i = 1, \dots, M$, $A_i$ appears earlier than $B_i$ in $P$.

If there is no such $P$, print -1.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq M \leq 2 \times 10^5$
• $1 \leq A_i, B_i \leq N$
• $A_i \neq B_i$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$

$A_1$ $B_1$

$\vdots$

$A_M$ $B_M$

Output

Print the answer.

Sample Input 1

4 3
2 1
3 4
2 4

Sample Output 1

2 1 3 4

The following five permutations $P$ satisfy the condition: $(2, 1, 3, 4), (2, 3, 1, 4), (2, 3, 4, 1), (3, 2, 1, 4), (3, 2, 4, 1)$. The lexicographically smallest among them is $(2, 1, 3, 4)$.

Sample Input 2

2 3
1 2
1 2
2 1

Sample Output 2

-1

No permutations $P$ satisfy the condition.

update @ 2024/3/10 09:49:28