Problem Statement

Given is a directed graph $G$ with $N$ vertices and $M$ edges. The vertices are numbered $1$ to $N$, and the $i$-th edge is directed from Vertex $A_i$ to Vertex $B_i$. It is guaranteed that the graph contains no self-loops or multiple edges.

Determine whether there exists an induced subgraph (see Notes) of $G$ such that the in-degree and out-degree of every vertex are both $1$. If the answer is yes, show one such subgraph. Here the null graph is not considered as a subgraph.

Note

For a directed graph $G = (V, E)$, we call a directed graph $G' = (V', E')$ satisfying the following conditions an induced subgraph of $G$:

• $V'$ is a (non-empty) subset of $V$.
• $E'$ is the set of all the edges in $E$ that have both endpoints in $V'$.

Constraints

• $1 \leq N \leq 1000$
• $0 \leq M \leq 2000$
• $1 \leq A_i,B_i \leq N$
• $A_i \neq B_i$
• All pairs $(A_i, B_i)$ are distinct.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
A_2 B_2
:
A_M B_M

Output

If there is no induced subgraph of $G$ that satisfies the condition, print -1. Otherwise, print an induced subgraph of $G$ that satisfies the condition, in the following format:

K
v_1
v_2
:
v_K

This represents the induced subgraph of $G$ with $K$ vertices whose vertex set is $\{v_1, v_2, \ldots, v_K\}$. (The order of $v_1, v_2, \ldots, v_K$ does not matter.) If there are multiple subgraphs of $G$ that satisfy the condition, printing any of them is accepted.