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 CPP):

Solution:
#include <iostream>
#include <iomanip>
#include <algorithm>
#include <vector>
#include <queue>
using namespace std;
int n, m;
vector< vector< int > > edg;
vector< int > d;
int main(void){
    cin >> n >> m;
    edg.assign(n+1, vector<int>());
    for(int i=0;i<m;i++){
        int a, b;
        cin >> a >> b;
        edg[a].push_back(b);
        edg[b].push_back(a);
    }
    d.assign(n+1, -1);
    d[1] = 0;
    queue<int> q;
    q.push(1);
    while(!q.empty()){
        int v = q.front();
        q.pop();
        for(int w: edg[v]) if(d[w] == -1){d[w] = v; q.push(w);}
    }
    puts("Yes");
    for(int i=2;i<=n;i++) cout << d[i] << endl;
}