原题：
F2. Spanning Tree with One Fixed Degree
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
You are given an undirected unweighted connected graph consisting of n vertices and m edges. It is guaranteed that there are no self-loops or multiple edges in the given graph.
Your task is to find any spanning tree of this graph such that the degree of the first vertex (vertex with label 1 on it) is equal to D (or say that there are no such spanning trees). Recall that the degree of a vertex is the number of edges incident to it.
Input
The first line contains three integers n, m and D (2≤n≤2⋅10^5, n−1≤m≤min(2⋅10 ^5,n(n−1)/2),1≤D<n ) — the number of vertices, the number of edges and required degree of the first vertex, respectively.
The following m lines denote edges: edge i is represented by a pair of integers vi, ui (1≤vi,ui≤n, ui≠vi), which are the indices of vertices connected by the edge. There are no loops or multiple edges in the given graph, i. e. for each pair (vi,ui) there are no other pairs (vi,ui) or (ui,vi) in the list of edges, and for each pair (vi,ui) the condition vi≠ui is satisfied.
Output
If there is no spanning tree satisfying the condition from the problem statement, print “NO” in the first line.
Otherwise print “YES” in the first line and then print n−1 lines describing the edges of a spanning tree such that the degree of the first vertex (vertex with label 1 on it) is equal to D. Make sure that the edges of the printed spanning tree form some subset of the input edges (order doesn’t matter and edge (v,u) is considered the same as the edge (u,v)).
If there are multiple possible answers, print any of them.
Examples
Input
4 5 1
1 2
1 3
1 4
2 3
3 4
Output
YES
2 1
2 3
3 4
Input
4 5 3
1 2
1 3
1 4
2 3
3 4
Output
YES
1 2
1 3
4 1
Input
4 4 3
1 2
1 4
2 3
3 4
Output
NO
中文：
给你一个无向图，没有权值，现在让你找到一个最小生成树，这个最小生成树的第一个节点度为D。
代码：
思路：
先把第1个节点从图中切出来，剩余的节点计算有多少个连通分量，如果连通分量的个数大于D，或者D比连通分量连接到第一个节点边的数量还要大的时候，直接输出NO。
否则把这些连通分量当成节点，连接到1号节点D次即可。