Score: 400 points
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.
Determine whether there is a way to place signposts satisfying our objective, and print one such way if it exists.
Input is given from Standard Input in the following format:
N M A_1 B_1 : A_M B_M
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.
4 4 1 2 2 3 3 4 4 2
Yes 1 2 2
If we place the signposts as described in the sample output, the following happens:
Thus, the objective is satisfied.
6 9 3 4 6 1 2 4 5 3 4 6 1 5 6 2 4 5 5 6
Yes 6 5 5 1 1
If there are multiple solutions, any of them will be accepted.