Problem:
Score : 600 points

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.

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 1

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

Sample Output 1

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.

Sample Input 2

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

Sample Output 2

-1

There is no induced subgraph of G that satisfies the condition.

Sample Input 3

6 9
1 2
2 3
3 4
4 5
5 6
5 1
5 2
6 1
6 2

Sample Output 3

4
2
3
4
5

Solution in JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

module.exports=function(r){var e={};function t(n){if(e[n])return e[n].exports;var o=e[n]={i:n,l:!1,exports:{}};return r[n].call(o.exports,o,o.exports,t),o.l=!0,o.exports}return t.m=r,t.c=e,t.d=function(r,e,n){t.o(r,e)||Object.defineProperty(r,e,{enumerable:!0,get:n})},t.r=function(r){"undefined"!=typeof Symbol&&Symbol.toStringTag&&Object.defineProperty(r,Symbol.toStringTag,{value:"Module"}),Object.defineProperty(r,"__esModule",{value:!0})},t.t=function(r,e){if(1&e&&(r=t(r)),8&e)return r;if(4&e&&"object"==typeof r&&r&&r.__esModule)return r;var n=Object.create(null);if(t.r(n),Object.defineProperty(n,"default",{enumerable:!0,value:r}),2&e&&"string"!=typeof r)for(var o in r)t.d(n,o,function(e){return r[e]}.bind(null,o));return n},t.n=function(r){var e=r&&r.__esModule?function(){return r.default}:function(){return r};return t.d(e,"a",e),e},t.o=function(r,e){return Object.prototype.hasOwnProperty.call(r,e)},t.p="",t(t.s=0)}([function(r,e,t){t(1)(t(2).readFileSync("/dev/stdin","UTF-8").split("\n"))},function(r,e,t){"use strict";function n(r,e){return function(r){if(Array.isArray(r))return r}(r)||function(r,e){var t=[],n=!0,o=!1,u=void 0;try{for(var l,i=r[Symbol.iterator]();!(n=(l=i.next()).done)&&(t.push(l.value),!e||t.length!==e);n=!0);}catch(r){o=!0,u=r}finally{try{n||null==i.return||i.return()}finally{if(o)throw u}}return t}(r,e)||function(){throw new TypeError("Invalid attempt to destructure non-iterable instance")}()}r.exports=function(r){for(var e=n(r[0].split(" ").map(function(r){return Number(r)}),2),t=e[0],o=e[1],u=new Array(t),l=0;l<t;l++)u[l]=[];for(var i=0;i<o;i++){var f=n(r[i+1].split(" ").map(function(r){return Number(r)-1}),2),a=f[0],c=f[1];u[a].push(c)}for(var p=0;p<t;p++){var s=new Array(t).fill(!1);s[p]=1;for(var v=[{v:p,fl:s,k:1}];v.length>0;){var y=v.pop(),d=!0,b=!1,m=void 0;try{for(var g,h=u[y.v][Symbol.iterator]();!(d=(g=h.next()).done);d=!0){var x=g.value;if(x==p){console.log(y.k);for(var S=0;S<t;S++)1==y.fl[S]&&console.log(S+1);return}if(1!=y.fl[x]){var j=y.fl.concat();j[x]=1,v.push({v:x,fl:j,k:y.k+1})}}}catch(r){b=!0,m=r}finally{try{d||null==h.return||h.return()}finally{if(b)throw m}}}}console.log(-1)}},function(r,e){r.exports=require("fs")}]);