Contest Duration: - (local time) (100 minutes) Back to Home
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Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

あるところに、洞窟があります。

• その部屋から出発し、「いまいる部屋にある道しるべを見て、それが指す部屋に移動する」ことを繰り返すと、部屋 1 に最小の移動回数でたどり着く。

### 制約

• 入力はすべて整数
• 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)
• どの 2 部屋間も、通路をいくつか通って行き来できる

### 入力

N M
A_1 B_1
:
A_M B_M


### 入力例 1

4 4
1 2
2 3
3 4
4 2


### 出力例 1

Yes
1
2
2


• 部屋 2 から出発した場合 (2) \to 11 回移動することになり、これが最小です。
• 部屋 3 から出発した場合 (3) \to 2 \to 12 回移動することになり、これが最小です。
• 部屋 4 から出発した場合 (4) \to 2 \to 12 回移動することになり、これが最小です。

したがって、出力例のように道しるべを置けば目標を達成できます。

### 入力例 2

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


### 出力例 2

Yes
6
5
5
1
1


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.