102233: [AtCoder]ABC223 D - Restricted Permutation

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.

问题描述

在满足以下条件的序列$P$中，找到字典序最小的序列。

• 对于每个$i = 1, \dots, M$，$A_i$在$P$中出现在$B_i$之前。

如果没有这样的$P$，打印-1。

约束

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq M \leq 2 \times 10^5$
• $1 \leq A_i, B_i \leq N$
• $A_i \neq B_i$
• 输入中的所有值都是整数。

输入

从标准输入以以下格式获取输入：

$N$ $M$
$A_1$ $B_1$
$\vdots$
$A_M$ $B_M$

输出

打印答案。

样例输入1

4 3
2 1
3 4
2 4

样例输出1

2 1 3 4

满足条件的序列$P$有以下五个：$(2, 1, 3, 4), (2, 3, 1, 4), (2, 3, 4, 1), (3, 2, 1, 4), (3, 2, 4, 1)$。它们中字典序最小的是$(2, 1, 3, 4)$。

样例输入2

2 3
1 2
1 2
2 1

样例输出2

-1

没有满足条件的序列$P$。