object Main {
  import java.io.{BufferedReader, InputStream, InputStreamReader}
  import java.util.StringTokenizer
  import scala.reflect.ClassTag

  def main(args: Array[String]): Unit = {
    val out = new java.io.PrintWriter(System.out)
    new Main(out, new InputReader(System.in)).solve()
    out.flush()
  }

  private val oj = System.getenv("ATCODER_DEBUG") == null
  def DEBUG(f: => Unit): Unit = {
    if (!oj){ f }
  }
  def debug(as: Array[Boolean]): Unit = if (!oj){ debug(as.map(x => if(x) "1" else "0").mkString) }
  def debug(as: Array[Int]): Unit = if (!oj){ debug(as.mkString(" ")) }
  def debug(as: Array[Long]): Unit =if (!oj){ debug(as.mkString(" ")) }
  def debugDim(m: Array[Array[Int]]): Unit = if (!oj){
    REP(m.length) { i =>
      debug(m(i))
    }
  }
  def debugDimFlip(m: Array[Array[Long]]): Unit = if (!oj){
    REP(m(0).length) { j =>
      REP(m.length) { i =>
        System.err.print(m(i)(j))
        System.err.print(" ")
      }
      System.err.println()
    }
  }
  def debug(s: => String): Unit = DEBUG {
    System.err.println(s)
  }
  def debugL(num: => Long): Unit = DEBUG {
    System.err.println(num)
  }

  class InputReader(val stream: InputStream) {
    private val reader = new BufferedReader(new InputStreamReader(stream), 32768)
    private var tokenizer: StringTokenizer = _

    def next(): String = {
      while (tokenizer == null || !tokenizer.hasMoreTokens)
        tokenizer = new StringTokenizer(reader.readLine)
      tokenizer.nextToken
    }

    def nextInt(): Int = Integer.parseInt(next())
    def nextLong(): Long = java.lang.Long.parseLong(next())
    def nextChar(): Char = next().charAt(0)

    def ni(): Int = nextInt()
    def nl(): Long = nextLong()
    def nc(): Char = nextChar()
    def ns(): String = next()
    def ns(n: Int): Array[Char] = ns().toCharArray
    def na(n: Int, offset: Int = 0): Array[Int] = map(n)(_ => ni() + offset)
    def na2(n: Int, offset: Int = 0): (Array[Int], Array[Int]) = {
      val A1, A2 = Array.ofDim[Int](n)
      REP(n) { i =>
        A1(i) = ni() + offset
        A2(i) = ni() + offset
      }
      (A1, A2)
    }
    def nm(n: Int, m: Int): Array[Array[Int]] = {
      val A = Array.ofDim[Int](n, m)
      REP(n) { i =>
        REP(m) { j =>
          A(i)(j) = ni()
        }
      }
      A
    }
    def nal(n: Int): Array[Long] = map(n)(_ => nl())
    def nm_c(n: Int, m: Int): Array[Array[Char]] = map(n) (_ => ns(m))
  }

  def REP(n: Int, offset: Int = 0)(f: Int => Unit): Unit = {
    var i = offset
    val N = n + offset
    while(i < N) { f(i); i += 1 }
  }
  def REP_r(n: Int, offset: Int = 0)(f: Int => Unit): Unit = {
    var i = n - 1 + offset
    while(i >= offset) { f(i); i -= 1 }
  }
  def TO(from: Int, to: Int)(f: Int => Unit): Unit = {
    REP(to - from + 1, from) { i =>
      f(i)
    }
  }
  def map[@specialized A: ClassTag](n: Int, offset: Int = 0)(f: Int => A): Array[A] = {
    val res = Array.ofDim[A](n)
    REP(n)(i => res(i) = f(i + offset))
    res
  }

  def sumL(as: Array[Int]): Long = {
    var s = 0L
    REP(as.length)(i => s += as(i))
    s
  }
  def cumSum(as: Array[Int]): Array[Long] = {
    val cum = Array.ofDim[Long](as.length + 1)
    REP(as.length) { i =>
      cum(i + 1) = cum(i) + as(i)
    }
    cum
  }
}

class Main(out: java.io.PrintWriter, sc: Main.InputReader) {
  import sc._
  import Main._
  import java.util.Arrays.sort

  import scala.collection.mutable
  import math.{abs, max, min}
  import mutable.ArrayBuffer

  // toIntとか+7とかするならvalにしろ
  @inline private def MOD = 1000000007

  sealed trait Stat
  case object Default extends Stat
  case class VisitPoint(i: Int) extends Stat

  def solve(): Unit = {
    val N, M = ni()
    val (from, to) = na2(M, -1)
    val g = packWUGraph(N, from, to)
    val deg = map(N)(i => g(i).length)

    def junctions = deg.count(_ > 2)

    def removeCycle(): Unit = {
      val removed = Array.ofDim[Boolean](M)
      val s = deg.indexWhere(_ > 2)
      val t = deg.lastIndexWhere(_ > 2)
      debug(s"s:$s")
      debug(s"t:$t")

      val removes = ArrayBuffer[Int]()

      var v = s
      var stat: Stat = Default
      while(true) {
        debug(s"v:$v")
        var next = -1
        REP(g(v).length) { i =>
          val e = g(v)(i)
          if (next == -1 && !removed(e.id)) {
            next = e.to
            removed(e.id) = true
            removes += e.id
          }
        }
        assert(next != -1)
        v = next
        stat match {
          case Default =>
            if (v == s) {
              removes.foreach { i =>
                deg(from(i)) -= 1
                deg(to(i)) -= 1
              }
              return
            }
            if (v == t) stat = VisitPoint(removes.length)

          case VisitPoint(i) =>
            if (v == t) {
              removes.drop(i).foreach { i =>
                deg(from(i)) -= 1
                deg(to(i)) -= 1
              }
              return
            }
        }
      }
    }

    // オイラーパス　&& サイクルが１個と２このケースを除く
    val ok = deg.forall(_ % 2 == 0) &&
        // サイクルが交わる点が１こもないとサイクルは１こ
        junctions > 0 && {
      // サイクルが交わる点が２個で、かつサイクルを一つ取り除いた後に交わる点がなくなったらサイクルは２こ
      // それ以外は３個以上あるので合体して３個にできる
      junctions > 2 || {
        debug(deg)
        removeCycle()
        debug(deg)
        junctions > 0
      }
    }

    if (ok) out.println("Yes")
    else out.println("No")
  }

  case class Edge(to: Int, id: Int)
  type WUGraph = Array[Array[Edge]]
  /**
    * uwiのぱくり
    */
  def packWUGraph(n: Int, from: Array[Int], to: Array[Int]): WUGraph = {
    val g = new Array[Array[Edge]](n)
    val p = new Array[Int](n)
    val m = from.length
    REP(m)(i => p(from(i)) += 1)
    REP(m)(i => p(to(i)) += 1)
    REP(n)(i => g(i) = new Array(p(i)))
    REP(m) { i =>
      p(from(i)) -= 1
      g(from(i))(p(from(i))) = Edge(to(i), i)
      p(to(i)) -= 1
      g(to(i))(p(to(i))) = Edge(from(i), i)
    }
    g
  }

}