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.

-----Notes----- 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.

-----Sample Input----- 4 5 1 2 2 3 2 4 4 1 4 3

-----Sample Output----- 3 1 2 4

The induced subgraph of G whose vertex set is {1, 2, 4} has the edge set {(1, 2), (2, 4), (4, 1)}. The in-degree and out-degree of every vertex in this graph are both 1.