/** * date : 2020-12-10 19:12:52 */ #define NDEBUG using namespace std; // intrinstic #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include // utility namespace Nyaan { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; template using V = vector; template using VV = vector>; using vi = vector; using vl = vector; using vd = V; using vs = V; using vvi = vector>; using vvl = vector>; template struct P : pair { template P(Args... args) : pair(args...) {} using pair::first; using pair::second; T &x() { return first; } const T &x() const { return first; } U &y() { return second; } const U &y() const { return second; } P &operator+=(const P &r) { first += r.first; second += r.second; return *this; } P &operator-=(const P &r) { first -= r.first; second -= r.second; return *this; } P &operator*=(const P &r) { first *= r.first; second *= r.second; return *this; } P operator+(const P &r) const { return P(*this) += r; } P operator-(const P &r) const { return P(*this) -= r; } P operator*(const P &r) const { return P(*this) *= r; } }; using pl = P; using pi = P; using vp = V; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template int sz(const T &t) { return t.size(); } template void mem(T (&a)[N], int c) { memset(a, c, sizeof(T) * N); } template inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template int lb(const vector &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template int ub(const vector &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } constexpr long long TEN(int n) { long long ret = 1, x = 10; for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1); return ret; } template pair mkp(const T &t, const U &u) { return make_pair(t, u); } template vector mkrui(const vector &v, bool rev = false) { vector ret(v.size() + 1); if (rev) { for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1]; } else { for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; } return ret; }; template vector mkuni(const vector &v) { vector ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template vector mkord(int N, F f) { vector ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template vector reord(const vector &v, const vector &ord) { int N = v.size(); vector ret(N); for (int i = 0; i < N; i++) ret[i] = v[ord[i]]; return ret; }; template vector mkiota(int N) { vector ret(N); iota(begin(ret), end(ret), 0); return ret; } template vector mkinv(vector &v, int max_val = -1) { if (max_val < (int)v.size()) max_val = v.size() - 1; vector inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } } // namespace Nyaan // bit operation namespace Nyaan { __attribute__((target("popcnt"))) inline int popcnt(const u64 &a) { return _mm_popcnt_u64(a); } __attribute__((target("bmi"))) inline int lsb(const u64 &a) { return _tzcnt_u64(a); } __attribute__((target("bmi"))) inline int ctz(const u64 &a) { return _tzcnt_u64(a); } __attribute__((target("lzcnt"))) inline int msb(const u64 &a) { return 63 - _lzcnt_u64(a); } __attribute__((target("lzcnt"))) inline int clz64(const u64 &a) { return _lzcnt_u64(a); } template inline int gbit(const T &a, int i) { return (a >> i) & 1; } template inline void sbit(T &a, int i, bool b) { a ^= (gbit(a, i) == b ? 0 : (T(b) << i)); } constexpr long long PW(int n) { return 1LL << n; } constexpr long long MSK(int n) { return (1LL << n) - 1; } } // namespace Nyaan // inout namespace Nyaan { template ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } void in() {} template void in(T &t, U &... u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &... u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } void outr() {} template void outr(const T &t, const U &... u) { cout << t; outr(u...); } struct IoSetupNya { IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupnya; } // namespace Nyaan // debug namespace DebugImpl { template struct is_specialize : false_type {}; template struct is_specialize< U, typename conditional::type> : true_type {}; template struct is_specialize< U, typename conditional::type> : true_type {}; template struct is_specialize::value, void>> : true_type { }; void dump(const char& t) { cerr << t; } void dump(const string& t) { cerr << t; } template ::value, nullptr_t> = nullptr> void dump(const U& t) { cerr << t; } template void dump(const T& t, enable_if_t::value>* = nullptr) { string res; if (t == Nyaan::inf) res = "inf"; if (is_signed::value) if (t == -Nyaan::inf) res = "-inf"; if (sizeof(T) == 8) { if (t == Nyaan::infLL) res = "inf"; if (is_signed::value) if (t == -Nyaan::infLL) res = "-inf"; } if (res.empty()) res = to_string(t); cerr << res; } template void dump(const pair&); template void dump(const pair&); template void dump(const T& t, enable_if_t::value>* = nullptr) { cerr << "[ "; for (auto it = t.begin(); it != t.end();) { dump(*it); cerr << (++it == t.end() ? "" : ", "); } cerr << " ]"; } template void dump(const pair& t) { cerr << "( "; dump(t.first); cerr << ", "; dump(t.second); cerr << " )"; } template void dump(const pair& t) { cerr << "[ "; for (int i = 0; i < t.second; i++) { dump(t.first[i]); cerr << (i == t.second - 1 ? "" : ", "); } cerr << " ]"; } void trace() { cerr << endl; } template void trace(Head&& head, Tail&&... tail) { cerr << " "; dump(head); if (sizeof...(tail) != 0) cerr << ","; trace(forward(tail)...); } } // namespace DebugImpl #ifdef NyaanDebug #define trc(...) \ do { \ cerr << "## " << #__VA_ARGS__ << " = "; \ DebugImpl::trace(__VA_ARGS__); \ } while (0) #else #define trc(...) #endif // macro #define each(x, v) for (auto&& x : v) #define each2(x, y, v) for (auto&& [x, y] : v) #define all(v) (v).begin(), (v).end() #define rep(i, N) for (long long i = 0; i < (long long)(N); i++) #define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--) #define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++) #define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--) #define reg(i, a, b) for (long long i = (a); i < (b); i++) #define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--) #define repc(i, a, cond) for (long long i = (a); (cond); i++) #define enm(i, val, vec) \ for (long long i = 0; i < (long long)(vec).size(); i++) \ if (auto& val = vec[i]; false) \ ; \ else #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define inc(...) \ char __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define die(...) \ do { \ Nyaan::out(__VA_ARGS__); \ return; \ } while (0) namespace Nyaan { void solve(); } int main() { Nyaan::solve(); } // template struct Trie { struct Node { array nxt; vector idxs; int idx; char key; Node(char c) : idx(-1), key(c) { fill(nxt.begin(), nxt.end(), -1); } }; vector st; Trie(char c = '$') { st.emplace_back(c); } inline int &next(int i, int j) { return st[i].nxt[j]; } void add(const string &s, int x) { int pos = 0; for (int i = 0; i < (int)s.size(); i++) { int k = s[i] - margin; if (~next(pos, k)) { pos = next(pos, k); continue; } int npos = st.size(); next(pos, k) = npos; st.emplace_back(s[i]); pos = npos; } st[pos].idx = x; st[pos].idxs.emplace_back(x); } int find(const string &s) { int pos = 0; for (int i = 0; i < (int)s.size(); i++) { int k = s[i] - margin; if (next(pos, k) < 0) return -1; pos = next(pos, k); } return pos; } int move(int pos, char c) { assert(pos < (int)st.size()); return pos < 0 ? -1 : next(pos, c - margin); } int size() const { return st.size(); } int idx(int pos) { return pos < 0 ? -1 : st[pos].idx; } vector idxs(int pos) { return pos < 0 ? vector() : st[pos].idxs; } }; template struct AhoCorasick : Trie { using TRIE = Trie; using TRIE::next; using TRIE::st; using TRIE::TRIE; vector cnt; void build(int heavy = true) { int n = st.size(); cnt.resize(n); for (int i = 0; i < n; i++) { if (heavy) sort(st[i].idxs.begin(), st[i].idxs.end()); cnt[i] = st[i].idxs.size(); } queue que; for (int i = 0; i < (int)X; i++) { if (~next(0, i)) { next(next(0, i), X) = 0; que.emplace(next(0, i)); } else { next(0, i) = 0; } } while (!que.empty()) { auto &x = st[que.front()]; int fail = x.nxt[X]; cnt[que.front()] += cnt[fail]; que.pop(); for (int i = 0; i < (int)X; i++) { int &nx = x.nxt[i]; if (nx < 0) { nx = next(fail, i); continue; } que.emplace(nx); next(nx, X) = next(fail, i); if (heavy) { auto &idx = st[nx].idxs; auto &idy = st[next(fail, i)].idxs; vector idz; set_union(idx.begin(), idx.end(), idy.begin(), idy.end(), back_inserter(idz)); idx = idz; } } } } vector match(string s, int heavy = true) { vector res(heavy ? TRIE::size() : 1); int pos = 0; for (auto &c : s) { pos = next(pos, c - margin); if (heavy) for (auto &x : st[pos].idxs) res[x]++; else res[0] += cnt[pos]; } return res; } int count(int pos) { return cnt[pos]; } }; template struct LazyMontgomeryModInt { using mint = LazyMontgomeryModInt; using i32 = int32_t; using u32 = uint32_t; using u64 = uint64_t; static constexpr u32 get_r() { u32 ret = mod; for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret; return ret; } static constexpr u32 r = get_r(); static constexpr u32 n2 = -u64(mod) % mod; static_assert(r * mod == 1, "invalid, r * mod != 1"); static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30"); static_assert((mod & 1) == 1, "invalid, mod % 2 == 0"); u32 a; constexpr LazyMontgomeryModInt() : a(0) {} constexpr LazyMontgomeryModInt(const int64_t &b) : a(reduce(u64(b % mod + mod) * n2)){}; static constexpr u32 reduce(const u64 &b) { return (b + u64(u32(b) * u32(-r)) * mod) >> 32; } constexpr mint &operator+=(const mint &b) { if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod; return *this; } constexpr mint &operator-=(const mint &b) { if (i32(a -= b.a) < 0) a += 2 * mod; return *this; } constexpr mint &operator*=(const mint &b) { a = reduce(u64(a) * b.a); return *this; } constexpr mint &operator/=(const mint &b) { *this *= b.inverse(); return *this; } constexpr mint operator+(const mint &b) const { return mint(*this) += b; } constexpr mint operator-(const mint &b) const { return mint(*this) -= b; } constexpr mint operator*(const mint &b) const { return mint(*this) *= b; } constexpr mint operator/(const mint &b) const { return mint(*this) /= b; } constexpr bool operator==(const mint &b) const { return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a); } constexpr bool operator!=(const mint &b) const { return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a); } constexpr mint operator-() const { return mint() - mint(*this); } constexpr mint pow(u64 n) const { mint ret(1), mul(*this); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } constexpr mint inverse() const { return pow(mod - 2); } friend ostream &operator<<(ostream &os, const mint &b) { return os << b.get(); } friend istream &operator>>(istream &is, mint &b) { int64_t t; is >> t; b = LazyMontgomeryModInt(t); return (is); } constexpr u32 get() const { u32 ret = reduce(a); return ret >= mod ? ret - mod : ret; } static constexpr u32 get_mod() { return mod; } }; template struct SuffixAutomaton { struct state { vector> next; uint64_t hit; int len, link, origin; char key; bool sorted; state() : hit(0), len(0), link(-1), origin(-1), key(0), sorted(false) {} state(int l, char k) : hit(0), len(l), link(-1), origin(-1), key(k), sorted(false) {} __attribute__((target("popcnt"))) int find(char c) const { c -= margin; if (((hit >> c) & 1) == 0) return -1; if (sorted) { return _mm_popcnt_u64(hit & ((1ull << c) - 1)); } else { c += margin; for (int i = 0; i < (int)next.size(); i++) { if (next[i].first == c) return i; } assert(0); } } inline int to(char c) const { int f = find(c); return ~f ? next[find(c)].second : -1; } void add(char c, int i) { c -= margin; assert(((hit >> c) & 1) == 0); next.emplace_back(c + margin, i); hit |= 1ull << c; } }; vector st; vector topo; SuffixAutomaton() = default; SuffixAutomaton(const string &S) { build(S); st.push_back(state()); } void build(const string &S) { int last = 0; for (int i = 0; i < (int)S.size(); i++) extend(S[i], last); tsort(); } [[deprecated]] void build(const vector &S) { for (auto &s : S) { int i = 0, last = 0; while (i < (int)s.size()) { int f = st[last].find(s[i]); if (f == -1) break; last = st[last].next[f].second; i++; } for (; i < (int)s.size(); i++) extend(s[i], last); } } int size() const { return st.size(); } int find(const string &s) const { int last = 0; for (auto &c : s) { int nx = st[last].find(c); if (nx == -1) return -1; last = st[last].next[nx].second; } return last; } state &operator[](int i) { return st[i]; } private: void extend(char c, int &last) { int cur = st.size(); st.emplace_back(st[last].len + 1, c); int p = last; for (; p != -1 && st[p].find(c) == -1; p = st[p].link) { st[p].add(c, cur); } if (p == -1) { st[cur].link = 0; } else { int q = st[p].to(c); if (st[p].len + 1 == st[q].len) st[cur].link = q; else { int clone = st.size(); { state cl = st[q]; cl.len = st[p].len + 1; cl.origin = q; st.push_back(std::move(cl)); } for (; p != -1; p = st[p].link) { int i = st[p].find(c); assert(i != -1); if (st[p].next[i].second != q) break; st[p].next[i].second = clone; } st[q].link = st[cur].link = clone; } } last = cur; } vector marked, temp; vector> buf; void dfs(int i) { temp[i] = 1; for (auto &[_, j] : st[i].next) if (!marked[j]) dfs(j); for (auto &j : buf[i]) if (!marked[j]) dfs(j); marked[i] = 1; topo.push_back(i); temp[i] = 0; } void tsort() { int n = st.size(); marked.resize(n), temp.resize(n), buf.resize(n); for (int i = 1; i < n; i++) buf[st[i].link].push_back(i); for (int i = 0; i < n; i++) if (!marked[i]) dfs(i); reverse(begin(topo), end(topo)); buf.clear(); buf.shrink_to_fit(); marked.clear(); marked.shrink_to_fit(); temp.clear(); temp.shrink_to_fit(); vector inv(n); for (int i = 0; i < n; i++) inv[topo[i]] = i; { vector st2; for (int i = 0; i < n; i++) st2.emplace_back(std::move(st[topo[i]])); st.swap(st2); } for (int i = 0; i < n; i++) { state &s = st[i]; sort(begin(s.next), end(s.next)); s.sorted = true; for (auto &[_, y] : s.next) y = inv[y]; if (s.link != -1) s.link = inv[s.link]; if (s.origin != -1) s.origin = inv[s.origin]; } topo.clear(); topo.shrink_to_fit(); } }; /** * @brief Suffix Automaton * @docs docs/string/suffix-automaton.md */ using mint = LazyMontgomeryModInt<1000000007>; using vm = vector; void Nyaan::solve() { inl(N, L, R); vl fs; { ll f = 1; ll g = 1; while (g <= R) { if (L <= g) fs.push_back(g); swap(f += g, g); } } vs ss; each(x, fs) ss.push_back(to_string(x)); AhoCorasick<10, '0'> aho; enm(i, s, ss) aho.add(s, i); aho.build(); vm dp(aho.size()); dp[0] = 1; rep(_, N) { vm nx(aho.size()); rep(i, sz(aho)) { if (aho.count(i)) continue; rep(j, 10) { auto n = aho.next(i, j); nx[n] += dp[i]; } } swap(dp, nx); } mint ans = 0; rep(i, sz(aho)) if (!aho.count(i)) ans += dp[i]; out(ans - 1); }