Problem:
Score : 500 points

Problem Statement

Takahashi is not good at problems about trees in programming contests, and Aoki is helping him practice.

First, Takahashi created a tree with N vertices numbered 1 through N, and wrote 0 at each edge.

Then, Aoki gave him M queries. The i-th of them is as follows:

Increment the number written at each edge along the path connecting vertices a_i and b_i, by one.

After Takahashi executed all of the queries, he told Aoki that, for every edge, the written number became an even number.
However, Aoki forgot to confirm that the graph Takahashi created was actually a tree, and it is possible that Takahashi made a mistake in creating a tree or executing queries.

Determine whether there exists a tree that has the property mentioned by Takahashi.

Constraints

2 ≤ N ≤ 10^5

1 ≤ M ≤ 10^5

1 ≤ a_i,b_i ≤ N

a_i ≠ b_i

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
:
a_M b_M

Output

Print YES if there exists a tree that has the property mentioned by Takahashi; print NO otherwise.

Sample Input 1

4 4
1 2
2 4
1 3
3 4

Sample Output 1

YES

For example, Takahashi's graph has the property mentioned by him if it has the following edges: 1-2, 1-3 and 1-4.
In this case, the number written at every edge will become 2.

Sample Input 2

5 5
1 2
3 5
5 1
3 4
2 3

Sample Output 2

NO

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

// yu!W 183


#include <bits/stdc++.h>
#include<string>
#define MAX_N 1000100

using namespace std;

#define ll long long
#define ull unsigned long long
#define ii pair<int,int>
#define iii pair<ii, int>

#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define ep emplace_back
#define sz(a) (int) a.size()
#define cl(a) a.clear()

#define vi vector<int>
#define vii vector<ii>

#define LOWBIT(x) ( (x) & -(x) )

#define FOR(x,a,b) for (int x=a;x<=b;x++)
#define FOD(x,a,b) for (int x=a;x>=b;x--)
#define REP(x,a,b) for (int x=a;x<b;x++)
#define RED(x,a,b) for (int x=a;x>b;x--)

const int MAX = 1e5 + 10;
const int MAXN = 1e4 + 10;
const ll MOD = 1e9 + 7;
const ll inf = 1e9;
const double pi = acos(-1.0);
const double eps = 1e-6;

int dx[] = {0 , -1 , 0 , 1};
int dy[] = {1 , 0 , -1 , 0};
//vector<int> a[100000];
int main()
{
 //freopen("t.txt","r",stdin);
 long long n,m;
 long long *a;cin>>n>>m; a= new long long[n+1];
 for (long long i=1;i<=n;i++) a[i]=0;
 while (m--){
 	int  x,y; cin>>x>>y;
 	a[x]++;
	a[y]++;
 }
 long long c= a[1];
 for (long long i=2;i<=n;i++){
 	if (c!=a[i]){
 		cout<<"NO"; return 0;
	 }
 }

 cout<<"YES";
}