Problem Statement

There are $N competitive programmers numbered person 1, person 2, \ldots$, and person N.
There is a relation called superiority between the programmers. For all pairs of distinct programmers (person X, person Y), exactly one of the following two relations holds: "person X is stronger than person Y" or "person Y is stronger than person X."
The superiority is transitive. In other words, for all triplets of distinct programmers (person X, person Y, person Z), it holds that:

• if person X is stronger than person Y and person Y is stronger than person Z, then person X is stronger than person Z.

A person X is said to be the strongest programmer if person X is stronger than person Y for all people Y other than person X. (Under the constraints above, we can prove that there is always exactly one such person.)
You have M pieces of information on their superiority. The i-th of them is that "person A_i is stronger than person B_i."
Can you determine the strongest programmer among the N based on the information?
If you can, print the person's number. Otherwise, that is, if there are multiple possible strongest programmers, print -1.

Input

The input is given from Standard Input in the following format:
N M
A_1 B_1
A_2 B_2
$\vdots$
A_M B_M

Output

If you can uniquely determine the strongest programmer, print the person's number; otherwise, print -1.

Constraints

• $2 \leq N \leq 50$
• $0 \leq M \leq \frac{N(N-1)}{2}$
• $1 \leq A_i, B_i \leq N$
• $A_i \neq B_i$
• If $i \neq j$, then $(A_i, B_i) \neq (A_j, B_j)$.
• There is at least one way to determine superiorities for all pairs of distinct programmers, that is consistent with the given information.

Sample Input 1

3 2
1 2
2 3

Sample Output 1

1

You have two pieces of information: "person 1 is stronger than person 2" and "person 2 is stronger than person 3."
By the transitivity, you can also infer that "person 1 is stronger than person 3," so person 1 is the strongest programmer.

Sample Input 2

3 2
1 3
2 3

Sample Output 2

-1

Both person 1 and person 2 may be the strongest programmer. Since you cannot uniquely determine which is the strongest, you should print -1.

Sample Input 3

6 6
1 6
6 5
6 2
2 3
4 3
4 2

Sample Output 3

-1

见题面 Input 部分

见题面 Output 部分