#pragma region Macros #pragma GCC optimize("O3") #pragma GCC target("avx2,avx") #pragma GCC optimize("unroll-loops") #include #define ll long long #define ld long double #define rep2(i, a, b) for(ll i = a; i <= b; ++i) #define rep(i, n) for(ll i = 0; i < n; ++i) #define rep3(i, a, b) for(ll i = a; i >= b; --i) #define pii pair #define pll pair #define pb push_back #define eb emplace_back #define vi vector #define vll vector #define vpi vector #define vpll vector #define overload2(_1, _2, name, ...) name #define vec(type, name, ...) vector name(__VA_ARGS__) #define VEC(type, name, size) \ vector name(size); \ IN(name) #define vv(type, name, h, ...) vector> name(h, vector(__VA_ARGS__)) #define VV(type, name, h, w) \ vector> name(h, vector(w)); \ IN(name) #define vvv(type, name, h, w, ...) vector>> name(h, vector>(w, vector(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector>>> name(a, vector>>(b, vector>(c, vector(__VA_ARGS__)))) #define fi first #define se second #define all(c) begin(c), end(c) #define lb(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define ub(c, x) distance((c).begin(), upper_bound(all(c), (x))) using namespace std; string YES[2] = {"NO", "YES"}; string Yes[2] = {"No", "Yes"}; string yes[2] = {"no", "yes"}; template using pq = priority_queue; template using pqg = priority_queue, greater>; #define si(c) (int)(c).size() #define INT(...) \ int __VA_ARGS__; \ IN(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ IN(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ IN(__VA_ARGS__) #define CHR(...) \ char __VA_ARGS__; \ IN(__VA_ARGS__) #define DBL(...) \ double __VA_ARGS__; \ IN(__VA_ARGS__) int scan() { return getchar(); } void scan(int &a) { cin >> a; } void scan(long long &a) { cin >> a; } void scan(char &a) { cin >> a; } void scan(double &a) { cin >> a; } void scan(string &a) { cin >> a; } template void scan(pair &p) { scan(p.first), scan(p.second); } template void scan(vector &); template void scan(vector &a) { for(auto &i : a) scan(i); } template void scan(T &a) { cin >> a; } void IN() {} template void IN(Head &head, Tail &... tail) { scan(head); IN(tail...); } template inline bool chmax(T &a, S b) { if(a < b) { a = b; return 1; } return 0; } template inline bool chmin(T &a, S b) { if(a > b) { a = b; return 1; } return 0; } vi iota(int n) { vi a(n); iota(all(a), 0); return a; } template vi iota(vector &a, bool greater = false) { vi res(a.size()); iota(all(res), 0); sort(all(res), [&](int i, int j) { if(greater) return a[i] > a[j]; return a[i] < a[j]; }); return res; } #define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()) vector factor(ll x) { vector ans; for(ll i = 2; i * i <= x; i++) if(x % i == 0) { ans.push_back({i, 1}); while((x /= i) % i == 0) ans.back().second++; } if(x != 1) ans.push_back({x, 1}); return ans; } template vector divisor(T x) { vector ans; for(T i = 1; i * i <= x; i++) if(x % i == 0) { ans.pb(i); if(i * i != x) ans.pb(x / i); } return ans; } template void zip(vector &x) { vector y = x; sort(all(y)); for(int i = 0; i < x.size(); ++i) { x[i] = lb(y, x[i]); } } int popcount(ll x) { return __builtin_popcountll(x); } struct Setup_io { Setup_io() { ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0); cout << fixed << setprecision(15); } } setup_io; int in() { int x; cin >> x; return x; } ll lin() { unsigned long long x; cin >> x; return x; } // template struct edge { // int from, to; // T cost; // int id; // edge(int to, T cost) : from(-1), to(to), cost(cost) {} // edge(int from, int to, T cost) : from(from), to(to), cost(cost) {} // edge(int from, int to, T cost, int id) : from(from), to(to), cost(cost), id(id) {} // edge &operator=(const int &x) { // to = x; // return *this; // } // operator int() const { return to; } // }; // template using Edges = vector>; // using Tree = vector>; // using Graph = vector>; // template using Wgraph = vector>>; // Graph getG(int n, int m = -1, bool directed = false, int margin = 1) { // Tree res(n); // if(m == -1) m = n - 1; // while(m--) { // int a, b; // cin >> a >> b; // a -= margin, b -= margin; // res[a].emplace_back(b); // if(!directed) res[b].emplace_back(a); // } // return move(res); // } // template Wgraph getWg(int n, int m = -1, bool directed = false, int margin = 1) { // Wgraph res(n); // if(m == -1) m = n - 1; // while(m--) { // int a, b; // T c; // cin >> a >> b >> c; // a -= margin, b -= margin; // res[a].emplace_back(b, c); // if(!directed) res[b].emplace_back(a, c); // } // return move(res); // } #define i128 __int128_t #define ull unsigned long long int #define TEST \ INT(testcases); \ while(testcases--) template ostream &operator<<(ostream &os, const vector &v) { for(auto &e : v) cout << e << " "; cout << endl; return os; } template ostream &operator<<(ostream &os, const pair &p) { cout << "(" << p.fi << ", " << p.se << ")"; return os; } template string to_string(pair p) { return "(" + to_string(p.first) + "," + to_string(p.second) + ")"; } template string to_string(A v) { if(v.empty()) return "{}"; string ret = "{"; for(auto &x : v) ret += to_string(x) + ","; ret.back() = '}'; return ret; } void dump() { cerr << endl; } template void dump(Head head, Tail... tail) { cerr << to_string(head) << " "; dump(tail...); } #define endl '\n' #ifdef _LOCAL #undef endl #define debug(x) \ cout << #x << ": "; \ dump(x) #else #define debug(x) #endif // mt19937 rng(chrono::steady_clock::now().time_since_epoch().count()); // int rnd(int n) { return uniform_int_distribution(0, n - 1)(rng); } // ll rndll(ll n) { return uniform_int_distribution(0, n - 1)(rng); } template static constexpr T inf = numeric_limits::max() / 2; #pragma endregion template struct TrieNode { int nxt[char_size]; int exist; vector accept; TrieNode() : exist(0) { memset(nxt, -1, sizeof(nxt)); } }; template struct Trie { using Node = TrieNode; vector nodes; int root; Trie() : root(0) { nodes.push_back(Node()); } void update_direct(int node, int id) { nodes[node].accept.push_back(id); } void update_child(int node, int child, int id) { ++nodes[node].exist; } void add(const string &str, int str_index, int node_index, int id) { if(str_index == str.size()) { update_direct(node_index, id); } else { const int c = str[str_index] - margin; if(nodes[node_index].nxt[c] == -1) { nodes[node_index].nxt[c] = (int)nodes.size(); nodes.push_back(Node()); } add(str, str_index + 1, nodes[node_index].nxt[c], id); update_child(node_index, nodes[node_index].nxt[c], id); } } void add(const string &str, int id) { add(str, 0, 0, id); } void add(const string &str) { add(str, nodes[0].exist); } void query(const string &str, const function &f, int str_index, int node_index) { for(auto &idx : nodes[node_index].accept) f(idx); if(str_index == str.size()) { return; } else { const int c = str[str_index] - margin; if(nodes[node_index].nxt[c] == -1) return; query(str, f, str_index + 1, nodes[node_index].nxt[c]); } } void query(const string &str, const function &f) { query(str, f, 0, 0); } int count() const { return (nodes[0].exist); } int size() const { return ((int)nodes.size()); } }; template struct AhoCorasick : Trie { using Trie::Trie; const int FAIL = char_size; vector correct; void build(bool heavy = true) { correct.resize(this->size()); for(int i = 0; i < this->size(); i++) { correct[i] = (int)this->nodes[i].accept.size(); } queue que; for(int i = 0; i <= char_size; i++) { if(~this->nodes[0].nxt[i]) { this->nodes[this->nodes[0].nxt[i]].nxt[FAIL] = 0; que.emplace(this->nodes[0].nxt[i]); } else { this->nodes[0].nxt[i] = 0; } } while(!que.empty()) { auto &now = this->nodes[que.front()]; correct[que.front()] += correct[now.nxt[FAIL]]; que.pop(); for(int i = 0; i < char_size; i++) { if(now.nxt[i] == -1) continue; int fail = now.nxt[FAIL]; while(this->nodes[fail].nxt[i] == -1) fail = this->nodes[fail].nxt[FAIL]; this->nodes[now.nxt[i]].nxt[FAIL] = this->nodes[fail].nxt[i]; if(heavy) { auto &u = this->nodes[now.nxt[i]].accept; auto &v = this->nodes[this->nodes[fail].nxt[i]].accept; vector accept; set_union(begin(u), end(u), begin(v), end(v), back_inserter(accept)); u = accept; } que.emplace(now.nxt[i]); } } } map match(const string &str, int now = 0) { map result; for(auto &c : str) { while(this->nodes[now].nxt[c - margin] == -1) now = this->nodes[now].nxt[FAIL]; now = this->nodes[now].nxt[c - margin]; for(auto &v : this->nodes[now].accept) result[v] += 1; } return result; } pair move(const char &c, int now) { int sum = 0; while(this->nodes[now].nxt[c - margin] == -1) now = this->nodes[now].nxt[FAIL]; now = this->nodes[now].nxt[c - margin]; sum += correct[now]; return {sum, now}; } }; namespace modular { constexpr ll MOD = 1000000007; const int MAXN = 1100000; template class modint; #define mint modint #define vmint vector vector Inv; mint inv(int x); template class modint { public: static constexpr int mod() { return Modulus; } ll a; constexpr modint(const ll x = 0) noexcept : a(((x % Modulus) + Modulus) % Modulus) {} constexpr ll &value() noexcept { return a; } constexpr const ll &value() const noexcept { return a; } constexpr modint operator-() const noexcept { return modint() - *this; } constexpr modint operator+() const noexcept { return *this; } constexpr modint &operator++() noexcept { if(++a == MOD) a = 0; return *this; } constexpr modint &operator--() noexcept { if(!a) a = MOD; a--; return *this; } constexpr modint operator++(int) { modint res = *this; ++*this; return res; } constexpr modint operator--(int) { mint res = *this; --*this; return res; } constexpr modint &operator+=(const modint rhs) noexcept { a += rhs.a; if(a >= Modulus) { a -= Modulus; } return *this; } constexpr modint &operator-=(const modint rhs) noexcept { if(a < rhs.a) { a += Modulus; } a -= rhs.a; return *this; } constexpr modint &operator*=(const modint rhs) noexcept { a = a * rhs.a % Modulus; return *this; } constexpr modint &operator/=(const modint rhs) noexcept { a = a * (modular::inv(rhs.a)).a % Modulus; return *this; } constexpr modint pow(long long n) const noexcept { modint x = *this, r = 1; while(n) { if(n & 1) r *= x; x *= x; n >>= 1; } return r; } constexpr modint inv() const noexcept { return pow(Modulus - 2); } constexpr friend modint operator+(const modint &lhs, const modint &rhs) { return modint(lhs) += modint(rhs); } constexpr friend modint operator-(const modint &lhs, const modint &rhs) { return modint(lhs) -= modint(rhs); } constexpr friend modint operator*(const modint &lhs, const modint &rhs) { return modint(lhs) *= modint(rhs); } constexpr friend modint operator/(const modint &lhs, const modint &rhs) { return modint(lhs) /= modint(rhs); } constexpr friend modint operator==(const modint &lhs, const modint &rhs) { return lhs.a == rhs.a; } constexpr friend modint operator!=(const modint &lhs, const modint &rhs) { return lhs.a != rhs.a; } // constexpr friend modint operator^=(const modint &lhs, const modint &rhs) { return modint(lhs) ^= modint(rhs); } }; vmint Fact{1, 1}, Ifact{1, 1}; mint inv(int n) { if(Inv.empty()) Inv.emplace_back(0), Inv.emplace_back(1); if(Inv.size() > n) return Inv[n]; else { for(int i = Inv.size(); i <= n; ++i) Inv.emplace_back(Inv[MOD % i] * (-MOD / i)); return Inv[n]; } } mint fact(int n) { if(Fact.size() > n) return Fact[n]; else for(int i = Fact.size(); i <= n; ++i) Fact.emplace_back(Fact[i - 1] * i); return Fact[n]; } mint ifact(int n) { if(Ifact.size() > n) return Ifact[n]; else for(int i = Ifact.size(); i <= n; ++i) Ifact.emplace_back(Ifact[i - 1] * inv(i)); return Ifact[n]; } mint modpow(ll a, ll n) { return mint(a).pow(n); } mint inv(mint a) { return inv(a.a); } mint ifact(mint a) { return ifact(a.a); } mint fact(mint a) { return fact(a.a); } mint modpow(mint a, ll n) { return modpow(a.a, n); } mint C(int a, int b) { if(a < 0 || b < 0) return 0; if(a < b) return 0; return fact(a) * ifact(b) * ifact(a - b); } mint P(int a, int b) { if(a < 0 || b < 0) return 0; if(a < b) return 0; return fact(a) * ifact(a - b); } ostream &operator<<(ostream &os, mint a) { os << a.a; return os; } istream &operator>>(istream &is, mint &a) { ll x; is >> x; a = x; return is; } struct modinfo { int mod, root; }; constexpr modinfo base0{1045430273, 3}; constexpr modinfo base1{1051721729, 6}; constexpr modinfo base2{1053818881, 7}; using mint0 = modint; using mint1 = modint; using mint2 = modint; using Poly = vmint; template void FMT(vector> &f, bool inv = false) { using V = vector>; static V g(30), ig(30); if(g.front().a == 0) { modint root = 2; while((root.pow((mod - 1) / 2)).a == 1) root += 1; rep(i, 30) g[i] = -(root.pow((mod - 1) >> (i + 2))), ig[i] = g[i].inv(); } int n = size(f); if(!inv) { for(int m = n; m >>= 1;) { modint w = 1; for(int s = 0, k = 0; s < n; s += 2 * m) { for(int i = s, j = s + m; i < s + m; ++i, ++j) { auto x = f[i], y = f[j] * w; if(x.a >= mod) x.a -= mod; f[i].a = x.a + y.a, f[j].a = x.a + (mod - y.a); } w *= g[__builtin_ctz(++k)]; } } } else { for(int m = 1; m < n; m *= 2) { modint w = 1; for(int s = 0, k = 0; s < n; s += 2 * m) { for(int i = s, j = s + m; i < s + m; ++i, ++j) { auto x = f[i], y = f[j]; f[i] = x + y, f[j].a = x.a + (mod - y.a), f[j] *= w; } w *= ig[__builtin_ctz(++k)]; } } } modint c; if(inv) c = modint(n).inv(); else c = 1; for(auto &&e : f) e *= c; } Poly operator-(Poly f) { for(auto &&e : f) e = -e; return f; } Poly &operator+=(Poly &l, const Poly &r) { l.resize(max(l.size(), r.size())); rep(i, r.size()) l[i] += r[i]; return l; } Poly operator+(Poly l, const Poly &r) { return l += r; } Poly &operator-=(Poly &l, const Poly &r) { l.resize(max(l.size(), r.size())); rep(i, r.size()) l[i] -= r[i]; return l; } Poly operator-(Poly l, const Poly &r) { return l -= r; } Poly &operator<<=(Poly &f, size_t n) { return f.insert(f.begin(), n, 0), f; } Poly operator<<(Poly f, size_t n) { return f <<= n; } Poly &operator>>=(Poly &f, size_t n) { return f.erase(f.begin(), f.begin() + min(f.size(), n)), f; } Poly operator>>(Poly f, size_t n) { return f >>= n; } constexpr int mod0 = 998244353, mod1 = 1300234241, mod2 = 1484783617; using M0 = modint; using M1 = modint; using M2 = modint; template void mul(vector> &l, vector> &r) { int n = size(l), m = size(r), sz = 1 << __lg(2 * (n + m - 1) - 1); l.resize(sz), FMT(l); r.resize(sz), FMT(r); rep(i, sz) l[i] *= r[i]; FMT(l, true); l.resize(n + m - 1); } Poly operator*(const Poly &l, const Poly &r) { if(l.empty() or r.empty()) return Poly(); int n = size(l), m = size(r), sz = 1 << __lg(2 * (n + m - 1) - 1); vector l0(n), r0(m); vector l1(n), r1(m); vector l2(n), r2(m); rep(i, n) l0[i] = l[i].a, l1[i] = l[i].a, l2[i] = l[i].a; rep(i, m) r0[i] = r[i].a, r1[i] = r[i].a, r2[i] = r[i].a; mul(l0, r0), mul(l1, r1), mul(l2, r2); Poly res(n + m - 1); // garner static constexpr M1 inv0 = 613999507; static constexpr M2 inv1 = 1147332803, inv0m1 = 45381342; static constexpr mint m0 = mod0, m0m1 = m0 * mod1; rep(i, n + m - 1) { int y0 = l0[i].a; int y1 = (inv0 * (l1[i] - y0)).a; int y2 = (inv0m1 * (l2[i] - y0) - inv1 * y1).a; res[i] = m0 * y1 + m0m1 * y2 + y0; } return res; } Poly &operator*=(Poly &l, const Poly &r) { return l = l * r; } Poly integ(const Poly &f) { Poly res(f.size() + 1); for(int i = 1; i < (int)res.size(); ++i) res[i] = f[i - 1] / i; return res; } struct Prd { deque deq; Prd() = default; void emplace(const Poly &f) { deq.emplace_back(f); } Poly calc() { if(deq.empty()) return {1}; sort(all(deq), [&](const Poly &f, const Poly &g) { return si(f) < si(g); }); while(deq.size() > 1) { deq.emplace_back(deq[0] * deq[1]); for(int i = 0; i < 2; ++i) deq.pop_front(); } return deq.front(); } }; Poly prd(vector &v) { Prd p; for(auto &e : v) p.emplace(e); return p.calc(); } // Poly deriv(const Poly &f) { // if(f.size() == 0) return Poly(); // Poly res(f.size() - 1); // rep(i, res.size()) res[i] = f[i + 1] * (i + 1); // return res; // } ostream &operator<<(ostream &os, const Poly &a) { for(auto e : a) cout << e.a << " "; return os; } } // namespace modular using namespace modular; int main() { INT(n); LL(L, R); AhoCorasick<10, '0'> trie; { ll p = 0, q = 1; while(p + q <= R) { swap(p, q); q = p + q; if(L <= q and q <= R) trie.add(to_string(q)); } } int m = trie.size(); trie.build(); vmint dp(m); dp[0] = 1; while(n--) { vmint nxt(m); rep(i, m) { for(char c = '0'; c <= '9'; ++c) { auto [p, q] = trie.move(c, i); if(!p) nxt[q] += dp[i]; } } swap(dp, nxt); } cout << accumulate(all(dp), (mint)0) - 1 << endl; }