Road Problem

### 题目描述 一张无向图有 $ n $ 个顶点，$ m $ 条边。求：至少加入几条边，使得图中任意两点间有两种不同的路径（不能经过同一条边，可以经过同一个顶点） ### 输入格式 第一行两个整数 $ n $ , $m$ 。( $2\leq n\leq$900 , $1\leq m\leq 100000 $ ) 之后 $m$ 行，每行两个整数 $u_{i}$ , $v_{i}$ ,表示一条无向边连接着编号为 $u_{i}$ , $v_{i}$ 的这两个点。 ### 输出格式 * 如果无解，输出 "-1" 。 * 如果不需要加边，输出 "0" 。 * 否则第一行一个整数 $a$ ,表示至少要加 $a$ 条边。接下来 $a$ 行，每行两个整数 $u_{i}$ , $v_{i}$ ，表示要加一条连接着编号为 $u_{i}$ , $v_{i}$ 的这两个点的无向边。（如果有多种解决方案，输出任意一个，新增边的输出顺序无要求。）

The Berland capital (as you very well know) contains $ n $ junctions, some pairs of which are connected by two-way roads. Unfortunately, the number of traffic jams in the capital has increased dramatically, that's why it was decided to build several new roads. Every road should connect two junctions. The city administration noticed that in the cities of all the developed countries between any two roads one can drive along at least two paths so that the paths don't share any roads (but they may share the same junction). The administration decided to add the minimal number of roads so that this rules was fulfilled in the Berland capital as well. In the city road network should exist no more than one road between every pair of junctions before or after the reform.

The first input line contains a pair of integers $ n $ , $ m $ ( $ 2<=n<=900,1<=m<=100000 $ ), where $ n $ is the number of junctions and $ m $ is the number of roads. Each of the following $ m $ lines contains a description of a road that is given by the numbers of the connected junctions $ a_{i},b_{i} $ ( $ 1<=a_{i},b_{i}<=n,a_{i}≠b_{i} $ ). The junctions are numbered from 1 to $ n $ . It is possible to reach any junction of the city from any other one moving along roads.

On the first line print $ t $ — the number of added roads. Then on $ t $ lines print the descriptions of the added roads in the format of the input data. You can use any order of printing the roads themselves as well as the junctions linked by every road. If there are several solutions to that problem, print any of them. If the capital doesn't need the reform, print the single number 0. If there's no solution, print the single number -1.

4 3
1 2
2 3
3 4

1
1 4

4 4
1 2
2 3
2 4
3 4

1
1 3