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 - 1people.
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.