# input
import sys
input = sys.stdin.readline
II = lambda : int(input())
MI = lambda : map(int, input().split())
LI = lambda : [int(a) for a in input().split()]
SI = lambda : input().rstrip()
LLI = lambda n : [[int(a) for a in input().split()] for _ in range(n)]
LSI = lambda n : [input().rstrip() for _ in range(n)]
MI_1 = lambda : map(lambda x:int(x)-1, input().split())
LI_1 = lambda : [int(a)-1 for a in input().split()]

mod = 998244353
inf = 1001001001001001001
ordalp = lambda s : ord(s)-65 if s.isupper() else ord(s)-97
ordallalp = lambda s : ord(s)-39 if s.isupper() else ord(s)-97
yes = lambda : print("Yes")
no = lambda : print("No")
yn = lambda flag : print("Yes" if flag else "No")

prinf = lambda ans : print(ans if ans < 1000001001001001001 else -1)
alplow = "abcdefghijklmnopqrstuvwxyz"
alpup = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
alpall = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"
URDL = {'U':(-1,0), 'R':(0,1), 'D':(1,0), 'L':(0,-1)}
DIR_4 = [[-1,0],[0,1],[1,0],[0,-1]]
DIR_8 = [[-1,0],[-1,1],[0,1],[1,1],[1,0],[1,-1],[0,-1],[-1,-1]]
DIR_BISHOP = [[-1,1],[1,1],[1,-1],[-1,-1]]
prime60 = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59]
sys.set_int_max_str_digits(0)
# sys.setrecursionlimit(10**6)
# import pypyjit
# pypyjit.set_param('max_unroll_recursion=-1')

from collections import defaultdict,deque
from heapq import heappop,heappush
from bisect import bisect_left,bisect_right
DD = defaultdict
BSL = bisect_left
BSR = bisect_right

class DSU:
    n : int 
    par : list[int]
    siz : list[int]
    fix_leader : bool
    __slots__ = ["n", "par", "siz", "fix_leader"]
    
    def __init__(self, n, fix_leader = False):
        self.n = n
        self.par = [*range(n)]
        self.siz = [1] * n
        self.fix_leader = fix_leader

    def leader(self, a):
        while self.par[a] != a:
            a = self.par[self.par[a]]
            self.par[a] = self.par[self.par[a]]
        return a

    def merge(self, a, b):
        a = self.leader(a)
        b = self.leader(b)
        if a == b: return a
        if self.fix_leader or self.siz[a] > self.siz[b]:
            self.siz[a] += self.siz[b]
            self.par[b] = a
            return a
        else:
            self.siz[b] += self.siz[a]
            self.par[a] = b
            return b

    def same(self, a, b):
        return self.leader(a) == self.leader(b)
    
    def size(self, a):
        return self.siz[self.leader(a)]
    
    def groups(self):
        res = [[] for i in range(self.n)]
        for i in range(self.n):
            res[self.leader(i)].append(i)
        res2 = []
        for i in range(self.n):
            if len(res[i]) > 0:
                res2.append(res[i])
        return res2

n, m = MI()

if n - 1 != m:
    no()
    exit()

uf = DSU(n)
d = [0] * n
e = [[] for i in range(n)]
for i in range(n - 1):
    a, b = MI_1()
    uf.merge(a, b)
    d[a] += 1
    d[b] += 1
    e[a].append(b)
    e[b].append(a)

g = uf.groups()

if len(g) >= 3:
    no()
    exit()

dc = [0] * 4
for i in range(n):
    if d[i] >= 4:
        no()
        exit()
    dc[d[i]] += 1


def check(e):
    d = [len(e[i]) for i in range(n)]
    for i in range(n):
        if d[i] >= 4:
            return False
    
    dis = [-1] * n
    st = []
    for u in range(n):
        if d[u] == 3:
            cnt = 0
            dis[u] = 0
            for v in e[u]:
                if d[v] == 3:
                    cnt += 1 
                else:
                    st.append(v)
                    dis[v] = 1
            if cnt != 2:
                return False
    
    leaf = []
    while st:
        u = st.pop()
        if len(e[u]) == 1:
            leaf.append(dis[u])
            continue
        f = 0
        for v in e[u]:
            if dis[v] == -1:
                f += 1
                dis[v] = dis[u] + 1
                st.append(v)
        
        if f == 0:
            return False
    
    if len(leaf) == 0:
        return False
    
    
    if all(leaf[0] == leaf[i] for i in range(len(leaf))):
        if leaf[0] >= 2:
            return True
    return False

from copy import deepcopy

if len(g) == 1:
    # 次数 3 の頂点 がパスをなすはず
    # そのとなりを探索すればじゅうぶん（４通り）
    
    dis = [inf] * n
    dd = []
    dd0 = []
    for u in range(n):
        if d[u] == 3:
            dis[u] = 0
            cnt = 0
            for v in e[u]:
                if d[v] == 3:
                    cnt += 1 
            if cnt == 1:
                add = []
                for v in e[u]:
                    if d[v] != 3:
                        add.append(v)
                dd.append(add)
            if cnt == 0:
                dd0 = e[u]
    
    if len(dd) >= 3:
        no()
        exit()
    
    if len(dd) == 2:
        for x in add[0]:
            for y in add[1]:
                e2 = deepcopy(e)
                e2[x].append(y)
                e2[y].append(x)
                if check(e2):
                    yes()
                    exit()
        no()
        exit()
        
    if len(dd0) == 3:
        for x in dd0:
            for y in dd0:
                if x == y: continue
                e2 = deepcopy(e)
                e2[x].append(y)
                e2[y].append(x)
                if check(e2):
                    yes()
                    exit()
        no()
        exit()
        
        
    no()
    exit()
    
if len(g) == 2:
    s0 = sum(d[i] for i in g[0])
    if 2 * s0 == g[0]:
        c = g[0]
        p = g[1]
    else:
        c = g[1]
        p = g[0]
    
    # p は path である必要がある
    if len(p) >= 2:
        cnt = 0
        for i in p:
            if d[i] == 1:
                cnt += 1
            elif d[i] == 2:
                pass
            else:
                no()
                exit()
        if cnt != 2:
            no()
            exit()
            
    # 次数 3 の頂点が サイクル
    # これに適当につなぐ
    dis = [inf] * n
    st = []
    for u in range(n):
        if d[u] == 3:
            cnt = 0
            dis[u] = 0
            for v in e[u]:
                if d[v] == 3:
                    cnt += 1 
                else:
                    st.append(v)
                    d[v] = 1
            if cnt != 2:
                no()
                exit()
    
    leaf = []
    while st:
        u = st.pop()
        if len(e[u]) == 1:
            leaf.append(dis[u])
            continue
        f = 0
        for v in e[u]:
            if dis[v] == -1:
                f += 1
                dis[v] = dis[u] + 1
                st.append(v)
        
        if f == 0:
            no()
            exit()
    
    leaf.sort()
    leaf[0] += len(p)
    
    if all(leaf[0] == leaf[i] for i in range(n)):
        if leaf[0] >= 2:
            yes()
            exit()
    no()
    exit()