101683: [AtCoder]ABC168 D - .. (Double Dots)

Memory Limit:256 MB Time Limit:2 S
Judge Style:Text Compare Creator:
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Description

Score: $400$ points

Problem Statement

There is a cave.

The cave has $N$ rooms and $M$ passages. The rooms are numbered $1$ to $N$, and the passages are numbered $1$ to $M$. Passage $i$ connects Room $A_i$ and Room $B_i$ bidirectionally. One can travel between any two rooms by traversing passages. Room $1$ is a special room with an entrance from the outside.

It is dark in the cave, so we have decided to place a signpost in each room except Room $1$. The signpost in each room will point to one of the rooms directly connected to that room with a passage.

Since it is dangerous in the cave, our objective is to satisfy the condition below for each room except Room $1$.

  • If you start in that room and repeatedly move to the room indicated by the signpost in the room you are in, you will reach Room $1$ after traversing the minimum number of passages possible.

Determine whether there is a way to place signposts satisfying our objective, and print one such way if it exists.

Constraints

  • All values in input are integers.
  • $2 \leq N \leq 10^5$
  • $1 \leq M \leq 2 \times 10^5$
  • $1 \leq A_i, B_i \leq N\ (1 \leq i \leq M)$
  • $A_i \neq B_i\ (1 \leq i \leq M)$
  • One can travel between any two rooms by traversing passages.

Input

Input is given from Standard Input in the following format:

$N$ $M$
$A_1$ $B_1$
$:$
$A_M$ $B_M$

Output

If there is no way to place signposts satisfying the objective, print No.

Otherwise, print $N$ lines. The first line should contain Yes, and the $i$-th line $(2 \leq i \leq N)$ should contain the integer representing the room indicated by the signpost in Room $i$.


Sample Input 1

4 4
1 2
2 3
3 4
4 2

Sample Output 1

Yes
1
2
2

If we place the signposts as described in the sample output, the following happens:

  • Starting in Room $2$, you will reach Room $1$ after traversing one passage: $(2) \to 1$. This is the minimum number of passages possible.
  • Starting in Room $3$, you will reach Room $1$ after traversing two passages: $(3) \to 2 \to 1$. This is the minimum number of passages possible.
  • Starting in Room $4$, you will reach Room $1$ after traversing two passages: $(4) \to 2 \to 1$. This is the minimum number of passages possible.

Thus, the objective is satisfied.


Sample Input 2

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

Sample Output 2

Yes
6
5
5
1
1

If there are multiple solutions, any of them will be accepted.

Input

题意翻译

在某个地方,有一个洞穴。 洞穴中有 $N$ 个房间和 $M$ 条通道,房间编号从 $1$ 到 $N$,通道编号从 $1$ 到 $M$。通道 $i$ 连接着房间 $A_i$ 和房间 $B_i$,可以双向通行。任何两个房间之间都可以通过一些通道来往。房间 $1$ 是一个特殊的房间,那里有洞穴的入口。 因为洞穴内部光线较暗,所以决定在房间1以外的每个房间都设置一个道标。每个房间的道标都会直接指向与该房间通过通道直接相连的一个房间。 由于洞穴内部很危险,对于房间 $1$ 以外的任何房间,目标都是满足以下条件: 从那个房间出发,反复进行"查看当前房间的道标,然后移动到它指向的房间"的操作,可以以最少的移动次数到达房间 $1$。 请判断是否存在可以达成目标的道标配置,如果存在,请输出一种这样的配置。

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