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<bits/stdc++.h>
using namespace std;
struct xy{
int x;int y;
};
int main(){
int n,m;cin >> n >> m;
vector<bool>vis(n,0);
queue<xy>q;
vector<vector<int>> adj(n);
vector<int>ans(n);
for(int i = 0;i<m;i++){
    int v,u;cin >> v >> u;
    v--;u--;
    adj[v].push_back(u);
    adj[u].push_back(v);
}
for(int i = 0;i<adj[0].size();i++) q.push({adj[0][i],0});
//vis[0] = 1;
while(!q.empty()){
    xy temp = q.front();q.pop();
    int v = temp.x;int u  = temp.y;
    if(vis[v]) continue;
    vis[v] = 1;
    ans[v] = u;
    for(int i = 0;i<adj[v].size();i++) q.push({adj[v][i],v});
}
cout <<"Yes"<<endl;
for(int i = 1;i<n;i++) cout << ans[i]+1<<endl;
return 0;
}