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.util.*;
 
public class Main {
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        String N = scan.next();
        int n = Integer.parseInt(N);
        String M = scan.next();
        int m = Integer.parseInt(M);
        
        ArrayList<ArrayList<Integer>> list = new ArrayList<ArrayList<Integer>>();

        for (int i = 0; i < n; i++) {
            list.add(new ArrayList<Integer>());
        }

        for (int i = 0; i < m; i++) {
            String A = scan.next();
            int a = Integer.parseInt(A);
            String B = scan.next();
            int b = Integer.parseInt(B);
            a--;
            b--;
            list.get(a).add(b);
            list.get(b).add(a);
        }
        //System.out.println(list);

        Queue<Integer> q = new ArrayDeque<>();

        ArrayList<Integer> dist = new ArrayList<Integer>();
        int depth = n;
        for (int i = 0; i < n; i++) {
            dist.add(n);
        }
        //System.out.println(dist);

        ArrayList<Integer> pre = new ArrayList<Integer>();
        for (int i = 0; i < n; i++) {
            pre.add(-1);
        }
        //System.out.println(pre);

        dist.set(0, 0);
        q.add(0);
        while (q.peek() != null) {
            int v = q.poll();
            for (int u: list.get(v)) {
                if (dist.get(u) != n) continue;
                dist.set(u, dist.get(v) + 1);
                pre.set(u, v);
                q.add(u);
            }
        }

        System.out.println("Yes");
        for (int i = 0; i < n; i++) {
            if (i == 0) continue;
            int ans = pre.get(i);
            ans++;
            System.out.println(ans);
        }
    }
}