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 sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        int[][] g = buildGraph(sc, n, m);
        int[] ans = new int[n];
        ArrayDeque<Integer> q = new ArrayDeque<>();
        boolean[] used = new boolean[n];
        used[0] = true;
        q.add(0);
        while(!q.isEmpty()){
            int v = q.poll();
            for(int nv : g[v]){
                if(used[nv]) continue;
                used[nv] = true;
                ans[nv] = v;
                q.add(nv);
            }
        }
        StringBuilder sb = new StringBuilder();
        sb.append("Yes\n");
        for (int i = 1; i < n; i++) {
            int v = ans[i] + 1;
            sb.append(v + "\n");
        }
        System.out.print(sb.toString());
        sc.close();

    }

    public static int[][] buildGraph(Scanner sc, int n, int m) {
        int[][] graph = new int[n][];
        int[][] edges = new int[m][2];
        int[] deg = new int[n];
        for (int i = 0; i < m; i++) {
            int a = sc.nextInt() - 1;
            int b = sc.nextInt() - 1;
            edges[i][0] = a;
            edges[i][1] = b;
            deg[a]++;
            deg[b]++;
        }
        for (int i = 0; i < n; i++) {
            graph[i] = new int[deg[i]];
        }
        for (int i = 0; i < m; i++) {
            int a = edges[i][0];
            int b = edges[i][1];
            graph[a][--deg[a]] = b;
            graph[b][--deg[b]] = a;
        }

        return graph;
    }

}