原題：
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：
給你一個無向圖，沒有權值，現在讓你找到一個最小生成樹，這個最小生成樹的第一個節點度爲D。
代碼：
思路：
先把第1個節點從圖中切出來，剩餘的節點計算有多少個連通分量，如果連通分量的個數大於D，或者D比連通分量連接到第一個節點邊的數量還要大的時候，直接輸出NO。
否則把這些連通分量當成節點，連接到1號節點D次即可。