A village has n people labelled 1..n. You are given a list of one-way trust relations: a pair a b means person a trusts person b.

There may be at most one arbiter. The arbiter is the person who

• trusts nobody, and
• is trusted by every one of the other n - 1 people.

Report the arbiter's label, or -1 if no such person exists.

Input format

Line 1: two integers n and m (the number of people and the number of trust relations). The next m lines each contain two integers a b, meaning person a trusts person b.

Output format

A single integer: the label of the arbiter, or -1 if there is none.

Constraints

• 1 <= n <= 200
• 0 <= m <= n * (n - 1)
• 1 <= a, b <= n and a != b
• No trust pair is listed more than once.

3 3
1 3
2 3
1 2

3

3 3
1 2
2 3
3 1

-1