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)

#include <bits/stdc++.h>

using namespace std;

#define pb push_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define all(a) (a).begin(),(a).end()
#define show(x) cerr << #x << " " << x << endl

typedef long long ll;
typedef unsigned long long ull;

constexpr const int INT_INF=0x3f3f3f3f; // 1061109567
constexpr const ll LL_INF=0x3f3f3f3f3f3f3f3f; // 4557430888798830399

template <typename T> bool chmin(T &a, T b) {
    if (a > b) {a = b;return true;}return false;
}

template <typename T> bool chmax(T &a, T b) {
    if (a < b) {a = b;return true;}return false;
}

// INT
#define GCD(a, b) __gcd(a, b)
template <typename T> T LCM(T a, T b) {return a / GCD(a, b) * b;}
template <typename T> T EXTGCD(T a, T b, T& x, T& y) {
    T d = a;
    if (b != 0) {d=EXTGCD(b,a%b,y,x);y-=(a/b)*x;}
    else x=1,y=0;
    return d;
}
template <typename T> bool is_prime(T a) {
    for(int i=2;i*i<=a;i++)if(a%i==0)return 1;
    return 0;
}

// MOD
const ll MOD = 1000000000 + 7;
#define add(a, b) ((a % MOD) + (b % MOD)) % MOD
#define mul(a, b) ((a % MOD) * (b % MOD)) % MOD
#define sub(a, b) ((a % MOD) + MOD - (b % MOD)) % MOD
template <typename T> T mod_inverse(T a, T mod, bool prime){ // if mod is prime, "prime" is true.
    if(prime){
        T tmp=mod-2,now=a,res=1;while(tmp){if(tmp&1)res=mul(res,now);now=mul(now,now);tmp>>=1;}
        return res;
    }else{T x,y;EXTGCD(a,mod,x,y);return (mod+x%mod)%mod;}
}
#define divide(a, b) ((a % MOD) * (mod_inverse(b, MOD, true))) % MOD

//LLの数値をつかう時は最後にLをつける癖をつけよう
//
//  　　┓　　　┏
//  　＊┗┓　┏┛
//  　　　┫　┣　＊
//  　┏┳┻━┻┳┓
//  　┗┫　　　┣┛
//  ＊　┣　　━┃　＊        Merry Christmas!!
//  　┏┛　　〃┃
//  　┃●　　　┣━┳┓
//  　┗┻┳━━┛　┣┛
//  　＊　┃┏┓┣┓┃
//WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW

const int maxn = 100001;
int a[maxn];
int n, m;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.precision(10);
    cout << fixed;
#ifdef LOCAL_DEFINE
    FILE *stream1;
    //FILE *stream2;
    stream1 = freopen("/Users/aim_cpo/CLionProjects/competitive/in.txt", "r", stdin);
    //stream2 = freopen("out.txt", "w", stdout);
    if (stream1 == nullptr) return 0;
    //if (stream2 == NULL) return 0;
#endif
    cin >> n >> m;
    for (int i = 0; i < n; i++) {
        int from, to; cin >> from >> to;
        a[from]++;
        a[to]++;
    }
    for (int i = 1; i <= n; i++) {
        if (a[i] & 1) {
            cout << "NO" << endl;
            return 0;
        }
    }
    cout << "YES" << endl;
#ifdef  LOCAL_DEFINE
    cerr << "Time elapsed: " << 1.0 * clock() / CLOCKS_PER_SEC << "s.\n";
#endif
    return 0;
}