#pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; //#define int long long typedef long long ll; typedef unsigned long long ul; typedef unsigned int ui; //ll mod = 1; constexpr ll mod = 998244353; //constexpr ll mod = 1000000009; const int mod17 = 1000000007; const ll INF = (ll)mod17 * mod17; typedef pairP; #define rep(i,n) for(int i=0;i=0;i--) #define Rep(i,sta,n) for(int i=sta;i=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) #define all(v) (v).begin(),(v).end() typedef pair LP; using ld = double; typedef pair LDP; const ld eps = 1e-10; const ld pi = acosl(-1.0); template void chmin(T& a, T b) { a = min(a, b); } template void chmax(T& a, T b) { a = max(a, b); } template vector vmerge(vector& a, vector& b) { vector res; int ida = 0, idb = 0; while (ida < a.size() || idb < b.size()) { if (idb == b.size()) { res.push_back(a[ida]); ida++; } else if (ida == a.size()) { res.push_back(b[idb]); idb++; } else { if (a[ida] < b[idb]) { res.push_back(a[ida]); ida++; } else { res.push_back(b[idb]); idb++; } } } return res; } template void cinarray(vector& v) { rep(i, v.size())cin >> v[i]; } template void coutarray(vector& v) { rep(i, v.size()) { if (i > 0)cout << " "; cout << v[i]; } cout << "\n"; } ll mod_pow(ll x, ll n, ll m = mod) { if (n < 0) { ll res = mod_pow(x, -n, m); return mod_pow(res, m - 2, m); } if (abs(x) >= m)x %= m; if (x < 0)x += m; //if (x == 0)return 0; ll res = 1; while (n) { if (n & 1)res = res * x % m; x = x * x % m; n >>= 1; } return res; } //mod should be <2^31 struct modint { int n; modint() :n(0) { ; } modint(ll m) { if (m < 0 || mod <= m) { m %= mod; if (m < 0)m += mod; } n = m; } operator int() { return n; } }; bool operator==(modint a, modint b) { return a.n == b.n; } bool operator<(modint a, modint b) { return a.n < b.n; } modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= (int)mod; return a; } modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += (int)mod; return a; } modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; } modint operator+(modint a, modint b) { return a += b; } modint operator-(modint a, modint b) { return a -= b; } modint operator*(modint a, modint b) { return a *= b; } modint operator^(modint a, ll n) { if (n == 0)return modint(1); modint res = (a * a) ^ (n / 2); if (n % 2)res = res * a; return res; } ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p); } modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); } modint operator/=(modint& a, modint b) { a = a / b; return a; } const int max_n = 1 << 20; modint fact[max_n], factinv[max_n]; void init_f() { fact[0] = modint(1); for (int i = 0; i < max_n - 1; i++) { fact[i + 1] = fact[i] * modint(i + 1); } factinv[max_n - 1] = modint(1) / fact[max_n - 1]; for (int i = max_n - 2; i >= 0; i--) { factinv[i] = factinv[i + 1] * modint(i + 1); } } modint comb(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[b] * factinv[a - b]; } modint combP(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[a - b]; } ll gcd(ll a, ll b) { a = abs(a); b = abs(b); if (a < b)swap(a, b); while (b) { ll r = a % b; a = b; b = r; } return a; } template void addv(vector& v, int loc, T val) { if (loc >= v.size())v.resize(loc + 1, 0); v[loc] += val; } /*const int mn = 2000005; bool isp[mn]; vector ps; void init() { fill(isp + 2, isp + mn, true); for (int i = 2; i < mn; i++) { if (!isp[i])continue; ps.push_back(i); for (int j = 2 * i; j < mn; j += i) { isp[j] = false; } } }*/ //[,val) template auto prev_itr(set& st, T val) { auto res = st.lower_bound(val); if (res == st.begin())return st.end(); res--; return res; } //[val,) template auto next_itr(set& st, T val) { auto res = st.lower_bound(val); return res; } using mP = pair; mP operator+(mP a, mP b) { return { a.first + b.first,a.second + b.second }; } mP operator+=(mP& a, mP b) { a = a + b; return a; } mP operator-(mP a, mP b) { return { a.first - b.first,a.second - b.second }; } mP operator-=(mP& a, mP b) { a = a - b; return a; } LP operator+(LP a, LP b) { return { a.first + b.first,a.second + b.second }; } LP operator+=(LP& a, LP b) { a = a + b; return a; } LP operator-(LP a, LP b) { return { a.first - b.first,a.second - b.second }; } LP operator-=(LP& a, LP b) { a = a - b; return a; } mt19937 mt(time(0)); const string drul = "DRUL"; string senw = "SENW"; //DRUL,or SENW //int dx[4] = { 1,0,-1,0 }; //int dy[4] = { 0,1,0,-1 }; //------------------------------------ template struct BIT { private: vector node; int n; public: void init(int n_) { n = n_; node.resize(n, 0); } //0-indexed void add(int a, T w) { for (int i = a; i < n; i |= i + 1)node[i] += w; } //[0,a) T sum(int a) { T ret = 0; for (int i = a - 1; i >= 0; i = (i & (i + 1)) - 1)ret += node[i]; return ret; } //[a,b) T sum(int a, int b) { return sum(b) - sum(a); } }; struct edge { int to; }; using edges = vector; using Graph = vector; struct HLDecomposition { struct Chain { int depth; P parent;//chain number,index vector

child;//child chain number,parent index vector mapfrom; BIT bt; Chain() { ; } Chain(int n) { bt.init(n); } }; Graph baseG; vector chains; vector

mapto;//raw index->chain number &index vector> mapfrom;//chain number & index ->raw index HLDecomposition() { ; } HLDecomposition(const Graph& g) { baseG = g; const int n = baseG.size(); mapto = vector

(n, P{ -1,-1 }); mapfrom.clear(); vector sz(n, 0); int start = 0; //int start = -1; //rep(i, n)if (baseG[i].size() <= 1) { start = i; break; } //assert(start != -1); size_check_bfs(start, sz); decomposition(start, start, 0, 0, 0, sz); } int depth(int t) { return chains[mapto[t].first].depth; } private: void size_check_bfs(int start, vector& sz) { const int n = baseG.size(); queue

que; que.push({ start,start }); int cnt = 0; vector ord(n, -1); while (!que.empty()) { int from, parent; tie(from, parent) = que.front(); que.pop(); ord[cnt++] = from; for (edge e : baseG[from]) { if (e.to == parent)continue; que.push({ e.to,from }); } } //assert(cnt == n); reverse(all(ord)); rep(i, n) { int from = ord[i]; sz[from] = 1; for (edge e : baseG[from])sz[from] += sz[e.to]; } } int decomposition(int from, int parent, int depth, int pnumber, int pindex, const vector& sz) { vector seq; bfs(from, parent, seq, sz); const int c = chains.size(); chains.push_back(Chain((int)seq.size())); //chains.push_back(Chain()); chains[c].depth = depth; chains[c].parent = { pnumber,pindex }; rep(i, seq.size()) { mapto[seq[i]] = { c,i }; chains[c].mapfrom.push_back(seq[i]); } mapfrom.push_back(chains[c].mapfrom); rep(i, seq.size()) { for (edge e : baseG[seq[i]]) { if (mapto[e.to].first != -1)continue; int nc = decomposition(e.to, seq[i], depth + 1, c, i, sz); chains[c].child.push_back({ nc,i }); } } return c; } void bfs(int from, int parent, vector& seq, const vector& sz) { for (;;) { seq.push_back(from); int best = -1, next = -1; for (edge e : baseG[from]) { if (e.to == parent)continue; if (best < sz[e.to]) { best = sz[e.to]; next = e.to; } } if (next == -1)break; parent = from; from = next; } } vector> all_edge(int u, int v) { vector> res; if (depth(u) > depth(v))swap(u, v); while (depth(v) > depth(u)) { res.push_back({ mapto[v].first,{ 0,mapto[v].second + 1 } }); P par = chains[mapto[v].first].parent; v = mapfrom[par.first][par.second]; } while (mapto[v].first != mapto[u].first) { res.push_back({ mapto[v].first,{ 0,mapto[v].second + 1 } }); P par = chains[mapto[v].first].parent; v = mapfrom[par.first][par.second]; res.push_back({ mapto[u].first,{ 0,mapto[u].second + 1 } }); par = chains[mapto[u].first].parent; u = mapfrom[par.first][par.second]; } P p = minmax(mapto[v].second, mapto[u].second); res.push_back({ mapto[v].first,{ p.first + 1,p.second + 1 } }); return res; } vector> all_vertice(int u, int v) { vector> res; if (depth(u) > depth(v))swap(u, v); while (depth(v) > depth(u)) { res.push_back({ mapto[v].first,{ 0,mapto[v].second + 1 } }); P par = chains[mapto[v].first].parent; v = mapfrom[par.first][par.second]; } while (mapto[v].first != mapto[u].first) { res.push_back({ mapto[v].first,{ 0,mapto[v].second + 1 } }); P par = chains[mapto[v].first].parent; v = mapfrom[par.first][par.second]; res.push_back({ mapto[u].first,{ 0,mapto[u].second + 1 } }); par = chains[mapto[u].first].parent; u = mapfrom[par.first][par.second]; } P p = minmax(mapto[v].second, mapto[u].second); res.push_back({ mapto[v].first,{ p.first,p.second + 1 } }); return res; } public: void add(int u, int a) { int id = mapto[u].first; int loc = mapto[u].second; chains[id].bt.add(loc, a); } modint query(int u, int v) { vector> vs = all_vertice(u, v); modint res = 0; rep(i, vs.size()) { int id = vs[i].first; int l = vs[i].second.first; int r = vs[i].second.second; res += chains[id].bt.sum(l, r); } return res; } }; struct lcagraph { private: int n; vector> G; vector> parent; vector depth; int root; int tmp; public: lcagraph(int n_) { n = n_; G.resize(n); parent.resize(n); depth.resize(n); tmp = 0; int cop = n; while (cop) { tmp++; cop /= 2; } rep(i, n)parent[i].resize(tmp); root = 0; } lcagraph() {} void init(int n_) { n = n_; G.resize(n); parent.resize(n); depth.resize(n); tmp = 0; int cop = n; while (cop) { tmp++; cop /= 2; } rep(i, n)parent[i].resize(tmp); root = 0; } void add_edge(int a, int b) { G[a].push_back(b); G[b].push_back(a); } void dfs(int id, int fr, int d) { parent[id][0] = fr; depth[id] = d; rep(j, G[id].size()) { int to = G[id][j]; if (to == fr)continue; dfs(to, id, d + 1); } } void complete(int r = 0) { root = r; dfs(root, -1, 0); rep(j, tmp - 1)rep(i, n) { if (parent[i][j] < 0)parent[i][j + 1] = -1; else parent[i][j + 1] = parent[parent[i][j]][j]; } } int lca(int u, int v) { if (depth[u] > depth[v])swap(u, v); for (int k = 0; k < tmp; k++) { if ((depth[v] - depth[u]) >> k & 1) { v = parent[v][k]; } } if (u == v)return u; for (int k = tmp - 1; k >= 0; k--) { if (parent[u][k] != parent[v][k]) { u = parent[u][k]; v = parent[v][k]; } } return parent[u][0]; } int dep(int x) { return depth[x]; } int dist(int x, int y) { int l = lca(x, y); return depth[x] + depth[y] - 2 * depth[l]; } //from a to b int proc_d(int a, int b, int d) { int l = lca(a, b); int res; if (dep(a) - dep(l) >= d) { res = a; rep(i, tmp) { if (d & (1 << i))res = parent[res][i]; } } else { d = dep(a) + dep(b) - 2 * dep(l) - d; res = b; rep(i, tmp) { if (d & (1 << i))res = parent[res][i]; } } return res; } }; void solve() { int n, m; cin >> n >> m; vector> G(n); rep(i, m) { int a, b; cin >> a >> b; a--; b--; G[a].push_back(b); G[b].push_back(a); } vector> g(n); vector> gg(n); vector par(n); rep(i, n)par[i] = i; function find_par = [&](int id) { if (par[id] == id)return id; return par[id] = find_par(par[id]); }; lcagraph lc(n); rep(i, n) { for (int to : G[i])if (i > to) { int p = find_par(to); if (p != i) { par[p] = i; g[i].push_back(p); gg[i].push_back({ p }); gg[p].push_back({ i }); lc.add_edge(i, p); } } } HLDecomposition hld(gg); lc.complete(n-1); vector trans(n); int tmp = 0; vector ri(n); function initdfs = [&](int id) { trans[id] = tmp; tmp++; for (int to : g[id]) { initdfs(to); } ri[id] = tmp; }; initdfs(n-1); auto comp = [&](int a,int b) { return trans[a] < trans[b]; }; modint ans = 0; rep(i, n) { modint val = 1; vector tos; for (int to : G[i]) { if (i > to)tos.push_back(to); } sort(all(tos),comp); vector rs; rs.push_back(i); for (int to : tos) { int l = lc.lca(rs.back(), to); while (rs.size()&&trans[l] <= trans[rs.back()] && trans[rs.back()] < ri[l]) { rs.pop_back(); } rs.push_back(l); int dif = lc.dep(to) - lc.dep(l); /*if (dif == 0) { cout << "! " << i << "\n"; coutarray(tos); }*/ assert(dif > 0); //cout << "? " << dif << "\n"; int p = lc.proc_d(to, l, dif - 1); val += hld.query(to, p); rs.push_back(to); //cout << "?? " << to << " " << p << " " << hld.query(to, p) << "\n"; } ans += val; hld.add(i, val); //cout << val << "\n"; //cout << "?\n"; //coutarray(tos); } cout << ans << "\n"; } signed main() { ios::sync_with_stdio(false); cin.tie(0); //cout << fixed<> t; rep(i, t) solve(); return 0; }