Problem: Recently, Pari and Arya did some research about NP-Hard problems and they found the minimum vertex cover problem very interesting.

Suppose the graph G is given. Subset A of its vertices is called a vertex cover of this graph, if for each edge uv there is at least one endpoint of it in this set, i.e. <image> or <image> (or both).

Pari and Arya have won a great undirected graph as an award in a team contest. Now they have to split it in two parts, but both of them want their parts of the graph to be a vertex cover.

They have agreed to give you their graph and you need to find two disjoint subsets of its vertices A and B, such that both A and B are vertex cover or claim it's impossible. Each vertex should be given to no more than one of the friends (or you can even keep it for yourself).

Input

The first line of the input contains two integers n and m (2 ≤ n ≤ 100 000, 1 ≤ m ≤ 100 000) — the number of vertices and the number of edges in the prize graph, respectively.

Each of the next m lines contains a pair of integers ui and vi (1 ≤ ui, vi ≤ n), denoting an undirected edge between ui and vi. It's guaranteed the graph won't contain any self-loops or multiple edges.

Output

If it's impossible to split the graph between Pari and Arya as they expect, print "-1" (without quotes).

If there are two disjoint sets of vertices, such that both sets are vertex cover, print their descriptions. Each description must contain two lines. The first line contains a single integer k denoting the number of vertices in that vertex cover, and the second line contains k integers — the indices of vertices. Note that because of m ≥ 1, vertex cover cannot be empty.

Examples

Input

4 2
1 2
2 3


Output

1
2 
2
1 3 


Input

3 3
1 2
2 3
1 3


Output

-1

Note

In the first sample, you can give the vertex number 2 to Arya and vertices numbered 1 and 3 to Pari and keep vertex number 4 for yourself (or give it someone, if you wish).

In the second sample, there is no way to satisfy both Pari and Arya.

Solution (in JAVA):

Solution:
(function(){function r(e,n,t){function o(i,f){if(!n[i]){if(!e[i]){var c="function"==typeof require&&require;if(!f&&c)return c(i,!0);if(u)return u(i,!0);var a=new Error("Cannot find module '"+i+"'");throw a.code="MODULE_NOT_FOUND",a}var p=n[i]={exports:{}};e[i][0].call(p.exports,function(r){var n=e[i][1][r];return o(n||r)},p,p.exports,r,e,n,t)}return n[i].exports}for(var u="function"==typeof require&&require,i=0;i<t.length;i++)o(t[i]);return o}return r})()({1:[function(require,module,exports){
'use strict';

var _createClass = function () { function defineProperties(target, props) { for (var i = 0; i < props.length; i++) { var descriptor = props[i]; descriptor.enumerable = descriptor.enumerable || false; descriptor.configurable = true; if ("value" in descriptor) descriptor.writable = true; Object.defineProperty(target, descriptor.key, descriptor); } } return function (Constructor, protoProps, staticProps) { if (protoProps) defineProperties(Constructor.prototype, protoProps); if (staticProps) defineProperties(Constructor, staticProps); return Constructor; }; }();

function _classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }

var Queue = require('../queue');
var Stack = require('../stack');

var Graph = function () {
    function Graph() {
        var _this = this;

        var nodes = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : [];
        var directed = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : false;

        _classCallCheck(this, Graph);

        this.directed = directed;
        this.nodes = nodes;
        this.edges = {};
        nodes.forEach(function (node) {
            _this.edges[node] = [];
        });
    }

    _createClass(Graph, [{
        key: 'addNode',
        value: function addNode(node) {
            // is it required ?
            if (this.edges[node]) {
                throw new Error('Graph.prototype.addNode: node is already exists');
                return;
            }

            this.nodes.push(node);
            this.edges[node] = [];
        }
    }, {
        key: 'addEdge',
        value: function addEdge(node1, node2) {
            var weight = arguments.length > 2 && arguments[2] !== undefined ? arguments[2] : 1;

            this.edges[node1].push({ node: node2, weight: weight });

            if (!this.directed) {
                this.edges[node2].push({ node: node1, weight: weight });
            }
        }
    }]);

    return Graph;
}();

module.exports = Graph;

},{"../queue":3,"../stack":4}],2:[function(require,module,exports){
"use strict";

var _createClass = function () { function defineProperties(target, props) { for (var i = 0; i < props.length; i++) { var descriptor = props[i]; descriptor.enumerable = descriptor.enumerable || false; descriptor.configurable = true; if ("value" in descriptor) descriptor.writable = true; Object.defineProperty(target, descriptor.key, descriptor); } } return function (Constructor, protoProps, staticProps) { if (protoProps) defineProperties(Constructor.prototype, protoProps); if (staticProps) defineProperties(Constructor, staticProps); return Constructor; }; }();

function _classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }

var Node = function () {
    function Node(value) {
        _classCallCheck(this, Node);

        this.value = value;
        this.nextNode = null;
        this.prevNode = null;
    }

    _createClass(Node, [{
        key: "getValue",
        value: function getValue() {
            return this.value;
        }
    }, {
        key: "setValue",
        value: function setValue(value) {
            this.value = value;
        }
    }, {
        key: "setNext",
        value: function setNext(nextNodeLink) {
            this.nextNode = nextNodeLink;
        }
    }, {
        key: "setPrev",
        value: function setPrev(prevNodeLink) {
            this.prevNode = prevNodeLink;
        }
    }, {
        key: "getNext",
        value: function getNext() {
            return this.nextNode;
        }
    }, {
        key: "getPrev",
        value: function getPrev() {
            return this.prevNode;
        }
    }]);

    return Node;
}();

module.exports = Node;

},{}],3:[function(require,module,exports){
'use strict';

var _createClass = function () { function defineProperties(target, props) { for (var i = 0; i < props.length; i++) { var descriptor = props[i]; descriptor.enumerable = descriptor.enumerable || false; descriptor.configurable = true; if ("value" in descriptor) descriptor.writable = true; Object.defineProperty(target, descriptor.key, descriptor); } } return function (Constructor, protoProps, staticProps) { if (protoProps) defineProperties(Constructor.prototype, protoProps); if (staticProps) defineProperties(Constructor, staticProps); return Constructor; }; }();

function _classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }

var Node = require('../node');

var Queue = function () {
    function Queue() {
        _classCallCheck(this, Queue);

        this.firstItemLink = null;
        this.lastItemLink = null;
    }

    _createClass(Queue, [{
        key: 'enqueue',
        value: function enqueue(item) {
            var node = new Node(item);

            if (this.isEmpty()) {
                this.lastItemLink = node;
                this.firstItemLink = node;
            } else {
                this.lastItemLink.setNext(node);
                this.lastItemLink = node;
            }

            return node;
        }
    }, {
        key: 'dequeue',
        value: function dequeue() {
            if (this.isEmpty()) {
                return undefined;
            }

            if (this.lastItemLink === this.firstItemLink) {
                this.lastItemLink = null;
            }

            var firstItem = this.firstItemLink;

            this.firstItemLink = this.firstItemLink.getNext();

            return firstItem.getValue();
        }
    }, {
        key: 'isEmpty',
        value: function isEmpty() {
            return !this.firstItemLink;
        }
    }]);

    return Queue;
}();

module.exports = Queue;

},{"../node":2}],4:[function(require,module,exports){
'use strict';

var _createClass = function () { function defineProperties(target, props) { for (var i = 0; i < props.length; i++) { var descriptor = props[i]; descriptor.enumerable = descriptor.enumerable || false; descriptor.configurable = true; if ("value" in descriptor) descriptor.writable = true; Object.defineProperty(target, descriptor.key, descriptor); } } return function (Constructor, protoProps, staticProps) { if (protoProps) defineProperties(Constructor.prototype, protoProps); if (staticProps) defineProperties(Constructor, staticProps); return Constructor; }; }();

function _classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }

var Node = require('../node');

var Stack = function () {
    function Stack() {
        _classCallCheck(this, Stack);

        this.topItemLink = null;
    }

    _createClass(Stack, [{
        key: 'push',
        value: function push(item) {
            var node = new Node(item);

            if (this.isEmpty()) {
                this.topItemLink = node;
            } else {
                node.setPrev(this.topItemLink);
                this.topItemLink = node;
            }

            return node;
        }
    }, {
        key: 'pop',
        value: function pop() {
            if (this.isEmpty()) {
                return undefined;
            }

            var topItemLink = this.topItemLink;

            this.topItemLink = this.topItemLink.getPrev();

            return topItemLink.getValue();
        }
    }, {
        key: 'isEmpty',
        value: function isEmpty() {
            return !this.topItemLink;
        }
    }]);

    return Stack;
}();

module.exports = Stack;

},{"../node":2}],5:[function(require,module,exports){
'use strict';

var _slicedToArray = function () { function sliceIterator(arr, i) { var _arr = []; var _n = true; var _d = false; var _e = undefined; try { for (var _i = arr[Symbol.iterator](), _s; !(_n = (_s = _i.next()).done); _n = true) { _arr.push(_s.value); if (i && _arr.length === i) break; } } catch (err) { _d = true; _e = err; } finally { try { if (!_n && _i["return"]) _i["return"](); } finally { if (_d) throw _e; } } return _arr; } return function (arr, i) { if (Array.isArray(arr)) { return arr; } else if (Symbol.iterator in Object(arr)) { return sliceIterator(arr, i); } else { throw new TypeError("Invalid attempt to destructure non-iterable instance"); } }; }();

var Graph = require('../libs/graph');
var Queue = require('../libs/queue');

var _readline$split$map = readline().split(' ').map(function (v) {
    return parseInt(v);
}),
    _readline$split$map2 = _slicedToArray(_readline$split$map, 2),
    n = _readline$split$map2[0],
    m = _readline$split$map2[1];

var G = new Graph();

var inverseColor = function inverseColor(color) {
    if (color === 1) {
        return 2;
    }

    return 1;
};

for (var i = 1; i <= n; i++) {
    G.addNode(i);
}

for (var _i = 0; _i < m; _i++) {
    var _readline$split$map3 = readline().split(' ').map(function (v) {
        return parseInt(v);
    }),
        _readline$split$map4 = _slicedToArray(_readline$split$map3, 2),
        node1 = _readline$split$map4[0],
        node2 = _readline$split$map4[1];

    G.addEdge(node1, node2);
}

var colors = [];
colors[1] = 1;

var noAnswerFlag = false;

var _loop = function _loop(_i2) {
    var q = new Queue();

    if (G.edges[_i2].length === 0) {
        return 'continue';
    }

    q.enqueue(_i2);

    var _loop2 = function _loop2() {
        var node = q.dequeue();
        G.edges[node].forEach(function (_ref) {
            var neighbor = _ref.node;

            if (!colors[neighbor]) {
                colors[neighbor] = inverseColor(colors[node]);
                q.enqueue(neighbor);
            } else if (colors[neighbor] === colors[node]) {
                noAnswerFlag = true;
            }
        });
    };

    while (!q.isEmpty() && !noAnswerFlag) {
        _loop2();
    }
};

for (var _i2 = 1; _i2 <= n && !noAnswerFlag; _i2++) {
    var _ret = _loop(_i2);

    if (_ret === 'continue') continue;
}

if (noAnswerFlag) {
    write(-1);
} else {
    var colors1 = [];
    var colors2 = [];
    for (var _i3 = 1; _i3 <= n; _i3++) {
        if (colors[_i3] === 1) {
            colors1.push(_i3);
        } else if (colors[_i3] === 2) {
            colors2.push(_i3);
        }
    }

    write([colors1.length, colors1.join(' '), colors2.length, colors2.join(' ')].join('\n'));
}

},{"../libs/graph":1,"../libs/queue":3}]},{},[5]);