Problem: 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.

Examples

Input

4 4
1 2
2 3
3 4
4 2


Output

Yes
1
2
2


Input

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


Output

Yes
6
5
5
1
1

Solution (in JAVA):

Solution:
import java.math.BigInteger;
import java.util.*;
import java.util.stream.Collectors;

public class Main {
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    long n = sc.nextLong();
    long m = sc.nextLong();
    Map<Long, Set<Long>> map = new TreeMap<>();
    Set<Long> all = new TreeSet<>();
    List<String> result = new ArrayList<>();
    for (long i = 0; i < n; i++) {
      map.put(i, new HashSet<>());
      all.add(i);
      if (i > 0) {
        result.add("0");
      }
    }
    for (long i = 0; i < m; i++) {
      long a = sc.nextLong() - 1;
      long b = sc.nextLong() - 1;
      map.get(a).add(b);
      map.get(b).add(a);
    }
    Set<Long> t = new TreeSet<>();
    t.add(0l);
    all.remove(0l);
    while (all.size() > 0) {
      Set<Long> newT = new TreeSet<>();
      t.forEach(a -> {
        Set<Long> s = map.get(a);
        s.forEach(b -> {
          if (all.contains(b)) {
            newT.add(b);
            all.remove(b);
            result.set((int) (b - 1), Long.toString(a + 1));
          }
        });
      });
      t = newT;
    }
    System.out.println("Yes\n" + result.stream().collect(Collectors.joining("\n")));
  }
}