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>
#define endl "\n"
#pragma GCC optimize("Ofast")  
#pragma GCC target("avx,avx2,fma") 
using namespace std;

int main(int argc, char const *argv[])
{
	int n, m; cin >> n >> m;
	vector<int> edge[n+1];
	for(int i=0; i<m ; i++) {
		int u, v; cin >> u >> v;
		edge[u].push_back(v);
		edge[v].push_back(u);
	}
	vector<int> ans(n+1);
	cout << "Yes" << endl;
	queue<int> q; q.push(1);
	unordered_set<int> hset;

	while(q.empty() == false) {
		int t = q.front(); q.pop();
		for(auto x : edge[t]) {
			if(hset.count(x) > 0) continue;
			ans[x] = t;
			q.push(x); hset.insert(x);
		}
	}
	for(int i=2 ; i<=n ; i++) cout << ans[i] << endl;
	return 0;
}