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.text.DecimalFormat;
import java.util.*;

public class Main {
    static int n = 0;
    static Set<Integer>[] paths = null;
    static int m = 0;
    static int[] a = null;
    static int[] b = null;
    static int[] depths = null;
    static int[] parents = null;
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        n = in.nextInt();
        paths = new Set[n+1];
        for(int i=1; i<=n; i++) {
            paths[i] = new HashSet<>();
        }
        m = in.nextInt();
        a = new int[m];
        b = new int[m];
        for(int i=0; i<m; i++) {
            a[i] = in.nextInt();
            b[i] = in.nextInt();
            paths[a[i]].add(b[i]);
            paths[b[i]].add(a[i]);
        }
        
        depths = new int[n+1];
        parents = new int[n+1];
        Queue<Integer> bfsQueue = new LinkedList<>();
        bfsQueue.add(1);
        boolean[] queued = new boolean[n+1];
        for(int i=0; i<=n; i++) {
            queued[i] = false;
        }
        queued[1] = true;
        while(bfsQueue.size()>0) {
            int target = bfsQueue.poll();
            int depth = depths[target];
            Iterator<Integer> childrenIT = paths[target].iterator();
            while(childrenIT.hasNext()) {
                int child = childrenIT.next();
                if(depths[child]>0 && depths[child]<=depth) {
                    continue;
                }
                if(queued[child]) {
                    continue;
                }
                depths[child] = depth+1;
                parents[child] = target;
                bfsQueue.add(child);
                queued[child] = true;
            }
            
        }
        
        System.out.println("Yes");
        for(int i=2; i<=n; i++) {
            System.out.println(parents[i]);
        }
    }
}