#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; #define ll long long #define ull unsigned long long #define rrep(i,m,n) for(ll (i)=(ll)(m);(i)>=(ll)(n);(i)--) #define rep(i,m,n) for(ll (i)=(ll)(m);i<(ll)(n);i++) #define REP(i,n) rep(i,0,n) #define FOR(i,c) for(decltype((c).begin())i=(c).begin();i!=(c).end();++i) #define all(hoge) (hoge).begin(),(hoge).end() typedef pair P; constexpr long double m_pi = 3.1415926535897932L; constexpr ll MOD = 1000000007; constexpr ll INF = 1LL << 61; constexpr long double EPS = 1e-10; template using vector2 = vector>; template using vector3 = vector>; typedef vector Array; typedef vector Matrix; string operator*(const string& s, int k) { if (k == 0) return ""; string p = (s + s) * (k / 2); if (k % 2 == 1) p += s; return p; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; } struct Edge {//グラフ int to, rev; ll cap; Edge(int _to, ll _cap, int _rev) { to = _to; cap = _cap; rev = _rev; } }; typedef vector Edges; typedef vector Graph; void add_edge(Graph& G, int from, int to, ll cap, bool revFlag, ll revCap) {//最大フロー求める Ford-fulkerson G[from].push_back(Edge(to, cap, (ll)G[to].size())); if (revFlag)G[to].push_back(Edge(from, revCap, (ll)G[from].size() - 1));//最小カットの場合逆辺は0にする } ll max_flow_dfs(Graph& G, ll v, ll t, ll f, vector& used) { if (v == t) return f; used[v] = true; for (int i = 0; i < G[v].size(); ++i) { Edge& e = G[v][i]; if (!used[e.to] && e.cap > 0) { ll d = max_flow_dfs(G, e.to, t, min(f, e.cap), used); if (d > 0) { e.cap -= d; G[e.to][e.rev].cap += d; return d; } } } return 0; } //二分グラフの最大マッチングを求めたりも出来る また二部グラフの最大独立集合は頂点数-最大マッチングのサイズ ll max_flow(Graph& G, ll s, ll t)//O(V(V+E)) { ll flow = 0; for (;;) { vector used(G.size()); REP(i, used.size())used[i] = false; ll f = max_flow_dfs(G, s, t, INF, used); if (f == 0) { return flow; } flow += f; } } void BellmanFord(Graph& G, ll s, Array& d, Array& negative) {//O(|E||V|) d.resize(G.size()); negative.resize(G.size()); REP(i, d.size())d[i] = INF; REP(i, d.size())negative[i] = false; d[s] = 0; REP(k, G.size() - 1) { REP(i, G.size()) { REP(j, G[i].size()) { if (d[i] != INF && d[G[i][j].to] > d[i] + G[i][j].cap) { d[G[i][j].to] = d[i] + G[i][j].cap; } } } } REP(k, G.size() - 1) { REP(i, G.size()) { REP(j, G[i].size()) { if (d[i] != INF && d[G[i][j].to] > d[i] + G[i][j].cap) { d[G[i][j].to] = d[i] + G[i][j].cap; negative[G[i][j].to] = true; } if (negative[i] == true)negative[G[i][j].to] = true; } } } } void Dijkstra(Graph& G, ll s, Array& d) {//O(|E|log|V|) d.resize(G.size()); REP(i, d.size())d[i] = INF; d[s] = 0; priority_queue, greater

> q; q.push(make_pair(0, s)); while (!q.empty()) { P a = q.top(); q.pop(); if (d[a.second] < a.first)continue; REP(i, G[a.second].size()) { Edge e = G[a.second][i]; if (d[e.to] > d[a.second] + e.cap) { d[e.to] = d[a.second] + e.cap; q.push(make_pair(d[e.to], e.to)); } } } } void WarshallFloyd(Graph& G, Matrix& d) {//O(V^3) d.resize(G.size()); REP(i, d.size())d[i].resize(G.size()); REP(i, d.size()) { REP(j, d[i].size()) { d[i][j] = ((i != j) ? INF : 0); } } REP(i, G.size()) { REP(j, G[i].size()) { chmin(d[i][G[i][j].to], G[i][j].cap); } } REP(i, G.size()) { REP(j, G.size()) { REP(k, G.size()) { chmin(d[j][k], d[j][i] + d[i][k]); } } } } bool tsort(Graph& graph, Array& order) {//トポロジカルソートO(E+V) int n = graph.size(), k = 0; Array in(n); for (auto& es : graph) for (auto& e : es)in[e.to]++; priority_queue> que; REP(i, n) if (in[i] == 0)que.push(i); while (que.size()) { int v = que.top(); que.pop(); order.push_back(v); for (auto& e : graph[v]) if (--in[e.to] == 0)que.push(e.to); } if (order.size() != n)return false; else return true; } class Lca { public: const int n = 0; const int log2_n = 0; std::vector> parent; std::vector depth; Lca() {} Lca(const Graph& g, int root) : n(g.size()), log2_n(log2(n) + 1), parent(log2_n, std::vector(n)), depth(n) { dfs(g, root, -1, 0); for (int k = 0; k + 1 < log2_n; k++) { for (int v = 0; v < (int)g.size(); v++) { if (parent[k][v] < 0) parent[k + 1][v] = -1; else parent[k + 1][v] = parent[k][parent[k][v]]; } } } void dfs(const Graph& g, int v, int p, int d) { parent[0][v] = p; depth[v] = d; for (auto& e : g[v]) { if (e.to != p) dfs(g, e.to, v, d + 1); } } int get(int u, int v) { if (depth[u] > depth[v]) std::swap(u, v); for (int k = 0; k < log2_n; k++) { if ((depth[v] - depth[u]) >> k & 1) { v = parent[k][v]; } } if (u == v) return u; for (int k = log2_n - 1; k >= 0; k--) { if (parent[k][u] != parent[k][v]) { u = parent[k][u]; v = parent[k][v]; } } return parent[0][u]; } }; void visit(const Graph& g, int v, vector>& scc, stack& S, vector& inS, vector& low,vector& num, int& time) { low[v] = num[v] = ++time; S.push(v); inS[v] = true; FOR(e, g[v]) { int w = e->to; if (num[w] == 0) { visit(g, w, scc, S, inS, low, num, time); low[v] = min(low[v], low[w]); } else if (inS[w]) low[v] = min(low[v], num[w]); } if (low[v] == num[v]) { scc.push_back(vector()); while (1) { int w = S.top(); S.pop(); inS[w] = false; scc.back().push_back(w); if (v == w) break; } } } void stronglyConnectedComponents(const Graph& g, vector>& scc) {//強連結成分分解 O(E+V) const int n = g.size(); vector num(n), low(n); stack S; vector inS(n); int time = 0; REP(u, n) if (num[u] == 0) visit(g, u, scc, S, inS, low, num, time); } class UnionFind { vector data; ll num; public: UnionFind(int size) : data(size, -1), num(size) { } bool unite(int x, int y) {//xとyの集合を統合する x = root(x); y = root(y); if (x != y) { if (data[y] < data[x]) swap(x, y); data[x] += data[y]; data[y] = x; } num -= (x != y); return x != y; } bool findSet(int x, int y) {//xとyが同じ集合か返す return root(x) == root(y); } int root(int x) {//xのルートを返す return data[x] < 0 ? x : data[x] = root(data[x]); } ll size(int x) {//xの集合のサイズを返す return -data[root(x)]; } ll numSet() {//集合の数を返す return num; } }; template class SegmentTree { private: T identity; F merge; ll n; vector dat; public: SegmentTree(F f, T id,vector v) :merge(f), identity(id) { int _n = v.size(); n = 1; while (n < _n)n *= 2; dat.resize(2 * n - 1, identity); REP(i, _n)dat[n + i - 1] = v[i]; for (int i = n - 2; i >= 0; i--)dat[i] = merge(dat[i * 2 + 1], dat[i * 2 + 2]); } SegmentTree(F f, T id, int _n) :merge(f), identity(id) { n = 1; while (n < _n)n *= 2; dat.resize(2 * n - 1, identity); } void set_val(int i, T x) { i += n - 1; dat[i] = x; while (i > 0) { i = (i - 1) / 2; dat[i] = merge(dat[i * 2 + 1], dat[i * 2 + 2]); } } T query(int l, int r) { T left = identity, right = identity; l += n - 1; r += n - 1; while (l < r) { if ((l & 1) == 0)left = merge(left, dat[l]); if ((r & 1) == 0)right = merge(dat[r - 1], right); l = l / 2; r = (r - 1) / 2; } return merge(left, right); } }; class SumSegTree { public: ll n, height; vector dat; // 初期化(_nは最大要素数) SumSegTree(ll _n) { n = 1; height = 1; while (n < _n) { n *= 2; height++; } dat = vector(2 * n - 1, 0); } // 場所i(0-indexed)にxを足す void add(ll i, ll x) { i += n - 1; // i番目の葉ノードへ dat[i] += x; while (i > 0) { // 下から上がっていく i = (i - 1) / 2; dat[i] += x; } } // 区間[l,r)の総和 ll sum(ll l, ll r) { ll ret = 0; l += n - 1; r += n - 1; while (l < r) { if ((l & 1) == 0)ret += dat[l]; if ((r & 1) == 0)ret += dat[r - 1]; l = l / 2; r = (r - 1) / 2; } return ret; } }; class RmqTree { private: ll _find(ll a, ll b, ll k, ll l, ll r) { if (r <= a || b <= l)return INF; // 交差しない if (a <= l && r <= b)return dat[k]; // a,l,r,bの順で完全に含まれる else { ll s1 = _find(a, b, 2 * k + 1, l, (l + r) / 2); // 左の子 ll s2 = _find(a, b, 2 * k + 2, (l + r) / 2, r); // 右の子 return min(s1, s2); } } public: ll n, height; vector dat; // 初期化(_nは最大要素数) RmqTree(ll _n) { n = 1; height = 1; while (n < _n) { n *= 2; height++; } dat = vector(2 * n - 1, INF); } // 場所i(0-indexed)をxにする void update(ll i, ll x) { i += n - 1; // i番目の葉ノードへ dat[i] = x; while (i > 0) { // 下から上がっていく i = (i - 1) / 2; dat[i] = min(dat[i * 2 + 1], dat[i * 2 + 2]); } } // 区間[a,b)の最小値。ノードk=[l,r)に着目している。 ll find(ll a, ll b) { return _find(a, b, 0, 0, n); } }; //約数求める //約数 void divisor(ll n, vector& ret) { for (ll i = 1; i * i <= n; i++) { if (n % i == 0) { ret.push_back(i); if (i * i != n) ret.push_back(n / i); } } sort(ret.begin(), ret.end()); } void prime_factorization(ll n, vector

& ret) { for (ll i = 2; i * i <= n; i++) { if (n % i == 0) { ret.push_back({ i,0 }); while (n % i == 0) { n /= i; ret[ret.size() - 1].second++; } } } if (n != 1)ret.push_back({ n,1 }); } ll mod_pow(ll x, ll n, ll mod) { ll res = 1; while (n > 0) { if (n & 1) res = res * x % mod; x = x * x % mod; n >>= 1; } return res; } ll mod_inv(ll x, ll mod) { return mod_pow(x, mod - 2, mod); } class Combination { public: Array fact; Array inv; ll mod; ll mod_inv(ll x) { ll n = mod - 2LL; ll res = 1LL; while (n > 0) { if (n & 1) res = res * x % mod; x = x * x % mod; n >>= 1; } return res; } //if n >= mod use lucas ll nCr(ll n, ll r) { if (n < r)return 0; if (n < mod)return ((fact[n] * inv[r] % mod) * inv[n - r]) % mod; ll ret = 1; while (n || r) { ll _n = n % mod, _r = r % mod; n /= mod; r /= mod; (ret *= nCr(_n, _r)) %= mod; } return ret; } ll nPr(ll n, ll r) { return (fact[n] * inv[n - r]) % mod; } ll nHr(ll n, ll r) { return nCr(r + n - 1, r); } Combination(ll _n, ll _mod) { mod = _mod; ll n = min(_n + 1, mod); fact.resize(n); fact[0] = 1; REP(i, n - 1) { fact[i + 1] = (fact[i] * (i + 1LL)) % mod; } inv.resize(n); inv[n - 1] = mod_inv(fact[n - 1]); for (int i = n - 1; i > 0; i--) { inv[i - 1] = inv[i] * i % mod; } } }; ll popcount(ll x) { x = (x & 0x5555555555555555) + (x >> 1 & 0x5555555555555555); x = (x & 0x3333333333333333) + (x >> 2 & 0x3333333333333333); x = (x & 0x0F0F0F0F0F0F0F0F) + (x >> 4 & 0x0F0F0F0F0F0F0F0F); x = (x & 0x00FF00FF00FF00FF) + (x >> 8 & 0x00FF00FF00FF00FF); x = (x & 0x0000FFFF0000FFFF) + (x >> 16 & 0x0000FFFF0000FFFF); x = (x & 0x00000000FFFFFFFF) + (x >> 32 & 0x00000000FFFFFFFF); return x; } class CentroidDecomposition { Graph& g; ll n; vector sz, dead; ll dfs(ll v, ll par) { sz[v] = 1; for (auto e : g[v]) if (e.to != par && !dead[e.to]) sz[v] += dfs(e.to, v); return sz[v]; } void find(ll v, ll par, ll tmp, Array& cs) { ll ok = 1; for (auto e : g[v]) { if (e.to == par || dead[e.to]) continue; find(e.to, v, tmp, cs); ok &= (sz[e.to] <= tmp / 2); } ok &= (tmp - sz[v] <= tmp / 2); if (ok) cs.push_back(v); }; public: CentroidDecomposition(Graph& _g) :g(_g),n(g.size()),sz(n, 1), dead(n, 0) {} vector build(ll r) { ll tmp = dfs(r, -1); vector cs; find(r, -1, tmp, cs); return cs; } inline ll get_sz(ll v) { return sz[v]; } inline void disable(ll v) { dead[v] = 1; } inline void enable(ll v) { dead[v] = 0; } inline ll alive(ll v) { return !dead[v]; } }; ll garner(Array& xs, Array& mods) { int M = xs.size(); Array coeffs(M, 1), constants(M, 0); for (int i = 0; i < M - 1; ++i) { // coffs[i] * v + constants[i] == mr[i].val (mod mr[i].first) を解く ll v = (xs[i] - constants[i] + mods[i]) % mods[i]; v = (v * mod_pow(coeffs[i], mods[i] - 2, mods[i])) % mods[i]; for (int j = i + 1; j < M; j++) { constants[j] = (constants[j] + coeffs[j] * v) % mods[j]; coeffs[j] = (coeffs[j] * mods[i]) % mods[j]; } } return constants.back(); } template//特殊な素数と原始根 998244353のとき3 class NTT { private: template inline void bit_reverse(vector& a) { int n = a.size(); int i = 0; for (int j = 1; j < n - 1; ++j) { for (int k = n >> 1; k > (i ^= k); k >>= 1); if (j < i) swap(a[i], a[j]); } } void _ntt(vector& a, int sign) { const int n = a.size(); assert((n ^ (n & -n)) == 0); //n = 2^k long long tmp = (mod - 1) * mod_pow((ll)n, mod - 2, mod) % mod; // -1/n long long h = mod_pow(root, tmp, mod); // ^n√g if (sign == -1) h = mod_pow(h, mod - 2, mod); bit_reverse(a); for (ll m = 1; m < n; m <<= 1) { const ll m2 = 2 * m; long long _base = mod_pow((ll)h, (ll)(n / m2), mod); long long _w = 1; for (int x = 0; x < m; ++x) { for (ll s = x; s < n; s += m2) { long long u = a[s]; long long d = (a[s + m] * _w) % mod; a[s] = (u + d) % mod; a[s + m] = (u - d + mod) % mod; } _w = (_w * _base) % mod; } } } void ntt(vector& input) { _ntt(input, 1); } void intt(vector& input) { _ntt(input, -1); const long long n_inv = mod_pow((ll)input.size(), mod - 2, mod); for (auto& x : input) x = (x * n_inv) % mod; } public: // 畳み込み演算を行う vector convolution(const vector& a, const vector& b) { int result_size = a.size() + b.size() - 1; int n = 1; while (n < result_size) n <<= 1; vector _a = a, _b = b; _a.resize(n, 0); _b.resize(n, 0); ntt(_a); ntt(_b); for (int i = 0; i < n; ++i) _a[i] = (_a[i] * _b[i]) % mod; intt(_a); _a.resize(result_size); return _a; } }; vector convolution_ntt(vector& a, vector& b, long long mod = 1224736769LL) {//任意modでのntt for (auto& x : a) x %= mod; for (auto& x : b) x %= mod; //大きい素数使いたいとき 92709568269121LL NTT<167772161LL, 3> ntt1; NTT<469762049LL, 3> ntt2; NTT<1224736769LL, 3> ntt3; vector x1 = ntt1.convolution(a, b); vector x2 = ntt2.convolution(a, b); vector x3 = ntt3.convolution(a, b); vector ret(x1.size()); vector mods{ 167772161LL, 469762049LL, 1224736769LL,mod }; for (int i = 0; i < x1.size(); ++i) { vector xs{ x1[i], x2[i], x3[i],0 }; ret[i] = garner(xs, mods); } return ret; } int main() { ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); ll n; cin >> n ; n++; Array a(n), b(n); REP(i, n) cin >> a[i]; REP(i, n)cin >> b[i]; Array c = convolution_ntt(a, b, MOD); ll ans = 0; REP(i, n)(ans += c[i] % MOD) %= MOD; cout << ans << endl; return 0; }