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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using static Asakatsu20200321D.Input;

namespace Asakatsu20200321D
{
    static class Input
    {
        /// <summary>
        /// 1行の入力をTに応じてリストに変換する関数を返す
        /// </summary>
        static Func<string, List<T>> Cast<T>() => _ => _.Split(' ').Select(Convert<T>()).ToList();

        /// <summary>
        /// 1行の入力をTに応じて変換する関数を返す
        /// </summary>
        static Func<string, T> Convert<T>()
        {
            Type t = typeof(T);
            if (t == typeof(string)) return _ => (T) (object) _;
            if (t == typeof(int)) return _ => (T) (object) int.Parse(_);
            if (t == typeof(long)) return _ => (T) (object) long.Parse(_);
            if (t == typeof(double)) return _ => (T) (object) double.Parse(_);
            if (t == typeof(List<string>)) return _ => (T) (object) Cast<string>()(_);
            if (t == typeof(List<int>)) return _ => (T) (object) Cast<int>()(_);
            if (t == typeof(List<long>)) return _ => (T) (object) Cast<long>()(_);
            if (t == typeof(List<double>)) return _ => (T) (object) Cast<double>()(_);

            throw new NotSupportedException(t + "is not supported.");
        }

        static T Convert<T>(string s) => Convert<T>()(s);

        static string String() => Console.ReadLine();

        static List<string> String(long rowNumber) => new bool[rowNumber].Select(_ => String()).ToList();

        /// <summary>
        /// 1行の値の入力
        /// </summary>
        public static void Cin<T>(out T a) => a = Convert<List<T>>(String())[0];

        public static void Cin<T1, T2>(out T1 a1, out T2 a2)
        {
            var v = Convert<List<string>>(String());
            a1 = Convert<T1>(v[0]);
            a2 = Convert<T2>(v[1]);
        }

        public static void Cin<T1, T2, T3>(out T1 a1, out T2 a2, out T3 a3)
        {
            var v = Convert<List<string>>(String());
            a1 = Convert<T1>(v[0]);
            a2 = Convert<T2>(v[1]);
            a3 = Convert<T3>(v[2]);
        }

        public static void Cin<T1, T2, T3, T4>(out T1 a1, out T2 a2, out T3 a3, out T4 a4)
        {
            var v = Convert<List<string>>(String());
            a1 = Convert<T1>(v[0]);
            a2 = Convert<T2>(v[1]);
            a3 = Convert<T3>(v[2]);
            a4 = Convert<T4>(v[3]);
        }

        public static void Cin<T1, T2, T3, T4, T5>(out T1 a1, out T2 a2, out T3 a3, out T4 a4, out T5 a5)
        {
            var v = Convert<List<string>>(String());
            a1 = Convert<T1>(v[0]);
            a2 = Convert<T2>(v[1]);
            a3 = Convert<T3>(v[2]);
            a4 = Convert<T4>(v[3]);
            a5 = Convert<T5>(v[4]);
        }

        public static void Cin<T1, T2, T3, T4, T5, T6>(out T1 a1, out T2 a2, out T3 a3, out T4 a4, out T5 a5, out T6 a6)
        {
            var v = Convert<List<string>>(String());
            a1 = Convert<T1>(v[0]);
            a2 = Convert<T2>(v[1]);
            a3 = Convert<T3>(v[2]);
            a4 = Convert<T4>(v[3]);
            a5 = Convert<T5>(v[4]);
            a6 = Convert<T6>(v[5]);
        }

        /// <summary>
        /// 複数行の値の入力
        /// </summary>
        public static void Cin<T>(long n, out List<T> l) => l = String(n).Select(Convert<T>()).ToList();

        public static void Cin<T1, T2>(long n, out List<T1> l1, out List<T2> l2)
        {
            l1 = new List<T1>();
            l2 = new List<T2>();
            foreach (List<string> l in String(n).Select(Convert<List<string>>()))
            {
                l1.Add(Convert<T1>(l[0]));
                l2.Add(Convert<T2>(l[1]));
            }
        }

        public static void Cin<T1, T2, T3>(long n, out List<T1> l1, out List<T2> l2, out List<T3> l3)
        {
            l1 = new List<T1>();
            l2 = new List<T2>();
            l3 = new List<T3>();
            foreach (List<string> l in String(n).Select(Convert<List<string>>()))
            {
                l1.Add(Convert<T1>(l[0]));
                l2.Add(Convert<T2>(l[1]));
                l3.Add(Convert<T3>(l[2]));
            }
        }

        public static void Cin<T1, T2, T3, T4>(long n, out List<T1> l1, out List<T2> l2, out List<T3> l3,
            out List<T4> l4)
        {
            l1 = new List<T1>();
            l2 = new List<T2>();
            l3 = new List<T3>();
            l4 = new List<T4>();
            foreach (List<string> l in String(n).Select(Convert<List<string>>()))
            {
                l1.Add(Convert<T1>(l[0]));
                l2.Add(Convert<T2>(l[1]));
                l3.Add(Convert<T3>(l[2]));
                l4.Add(Convert<T4>(l[3]));
            }
        }

        /// <summary>
        /// 1行に書かれた複数の値の入力
        /// </summary>
        public static void Cin<T>(out List<T> lArr) => lArr = Convert<List<T>>(String());

        /// <summary>
        /// h行の行列の入力
        /// </summary>
        public static void Cin<T>(long h, out List<List<T>> map) => map = String(h).Select(Convert<List<T>>()).ToList();
    }

    class Program
    {
        public static void Main(string[] args)
        {
            StreamWriter streamWriter = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
            Console.SetOut(streamWriter);
            new Solver().Solve();
            Console.Out.Flush();
        }

        public static void Debug()
        {
            new Solver().Solve();
        }
    }

    class Solver
    {
        private long N;
        private long M;
        private List<long> A;
        private List<long> B;

        public void Solve()
        {
            Cin(out N, out M);
            Cin(M, out A, out B);

            Dictionary<long, int> cnt = new Dictionary<long, int>();
            for (int i = 0; i < M; i++)
            {
                if (!cnt.ContainsKey(A[i])) cnt.Add(A[i], 0);
                if (!cnt.ContainsKey(B[i])) cnt.Add(B[i], 0);

                cnt[A[i]]++;
                cnt[B[i]]++;
            }

            foreach (var v in cnt)
            {
                if (v.Value % 2 != 0)
                {
                    Console.WriteLine("No");
                    return;
                }
            }
            Console.WriteLine("Yes");
        }
    }
}