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.

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.

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.

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.

见题面 Input 部分

见题面 Output 部分