D - Restricted Permutation

Score : $400$ points

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.

4 3
2 1
3 4
2 4

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 $(2, 1, 3, 4)$.

2 3
1 2
1 2
2 1

-1

No permutations $P$ satisfy the condition.