#define MOD_TYPE 1 #pragma region Macros #include using namespace std; #if 0 #include #include using Int = boost::multiprecision::cpp_int; using lld = boost::multiprecision::cpp_dec_float_100; #endif #if 1 #pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #endif using ll = long long int; using ld = long double; using pii = pair; using pll = pair; using pld = pair; template using smaller_queue = priority_queue, greater>; constexpr ll MOD = (MOD_TYPE == 1 ? (ll)(1e9 + 7) : 998244353); //constexpr ll MOD = 1; constexpr int INF = (int)1e9 + 10; constexpr ll LINF = (ll)4e18; constexpr double PI = acos(-1.0); constexpr double EPS = 1e-9; constexpr int Dx[] = {0, 0, -1, 1, -1, 1, -1, 1, 0}; constexpr int Dy[] = {1, -1, 0, 0, -1, -1, 1, 1, 0}; #define REP(i, m, n) for (ll i = m; i < (ll)(n); ++i) #define rep(i, n) REP(i, 0, n) #define REPI(i, m, n) for (int i = m; i < (int)(n); ++i) #define repi(i, n) REPI(i, 0, n) #define MP make_pair #define MT make_tuple #define YES(n) cout << ((n) ? "YES" : "NO") << "\n" #define Yes(n) cout << ((n) ? "Yes" : "No") << "\n" #define possible(n) cout << ((n) ? "possible" : "impossible") << "\n" #define Possible(n) cout << ((n) ? "Possible" : "Impossible") << "\n" #define Yay(n) cout << ((n) ? "Yay!" : ":(") << "\n" #define all(v) v.begin(), v.end() #define NP(v) next_permutation(all(v)) #define dbg(x) cerr << #x << ":" << x << "\n"; struct io_init { io_init() { cin.tie(0); ios::sync_with_stdio(false); cout << setprecision(30) << setiosflags(ios::fixed); }; } io_init; 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; } inline ll CEIL(ll a, ll b) { return (a + b - 1) / b; } template inline void Fill(A (&array)[N], const T &val) { fill((T *)array, (T *)(array + N), val); } template constexpr istream &operator>>(istream &is, pair &p) noexcept { is >> p.first >> p.second; return is; } template constexpr ostream &operator<<(ostream &os, pair &p) noexcept { os << p.first << " " << p.second; return os; } #pragma endregion #pragma region mint template struct Fp { long long val; constexpr Fp(long long v = 0) noexcept : val(v % MOD) { if (val < 0) v += MOD; } constexpr int getmod() { return MOD; } constexpr Fp operator-() const noexcept { return val ? MOD - val : 0; } constexpr Fp operator+(const Fp &r) const noexcept { return Fp(*this) += r; } constexpr Fp operator-(const Fp &r) const noexcept { return Fp(*this) -= r; } constexpr Fp operator*(const Fp &r) const noexcept { return Fp(*this) *= r; } constexpr Fp operator/(const Fp &r) const noexcept { return Fp(*this) /= r; } constexpr Fp &operator+=(const Fp &r) noexcept { val += r.val; if (val >= MOD) val -= MOD; return *this; } constexpr Fp &operator-=(const Fp &r) noexcept { val -= r.val; if (val < 0) val += MOD; return *this; } constexpr Fp &operator*=(const Fp &r) noexcept { val = val * r.val % MOD; if (val < 0) val += MOD; return *this; } constexpr Fp &operator/=(const Fp &r) noexcept { long long a = r.val, b = MOD, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } val = val * u % MOD; if (val < 0) val += MOD; return *this; } constexpr bool operator==(const Fp &r) const noexcept { return this->val == r.val; } constexpr bool operator!=(const Fp &r) const noexcept { return this->val != r.val; } friend constexpr ostream &operator<<(ostream &os, const Fp &x) noexcept { return os << x.val; } friend constexpr istream &operator>>(istream &is, Fp &x) noexcept { return is >> x.val; } }; Fp modpow(const Fp &a, long long n) noexcept { if (n == 0) return 1; auto t = modpow(a, n / 2); t = t * t; if (n & 1) t = t * a; return t; } using mint = Fp; #pragma endregion template struct AhoCorasick { struct node { // suff : 先頭の文字を最小限消してグラフに存在する頂点にするときの行先の頂点 // dict : 先頭の文字を最小限消して辞書に存在する単語にするときの行先の頂点 // depth : Trie木における深さ(省略可能) // word_index : このノードで終わる最初の単語のindex(なければ-1) // word_count : このノードで終わる単語の総数 count_total_matches()で使用 // link : Trie及びsuffixの辺の接続先頂点(なければ-1) int suff = -1, dict = -1, depth = 0; int word_index = -1, word_count = 0; int link[ALPHABET]; node() { fill(link, link + ALPHABET, -1); } int &operator[](char c) { return link[c - MIN_CHAR]; } }; // nodes : 頂点集合 // W : 現在の単語数 // word_location : 各単語の(単語リストの)index // word_indices_by_depth : 単語のindexをdepthの降順に並べたもの // defer : 各単語のTrie木の最後の頂点のindex vector nodes; int W; vector word_location; vector word_indices_by_depth; vector defer; AhoCorasick(const vector &words = {}) { if (!words.empty()) build(words); } int get_or_add_child(int current, char c) { if (nodes[current][c] >= 0) return nodes[current][c]; int index = int(nodes.size()); nodes[current][c] = index; nodes.emplace_back(); nodes.back().depth = nodes[current].depth + 1; return index; } int add_word(const string &word, int word_index) { assert(!nodes.empty()); int current = 0; for (char c : word) current = get_or_add_child(current, c); if (nodes[current].word_index < 0) nodes[current].word_index = word_index; nodes[current].word_count++; return current; } // locationからcを追加したときの行き先 O(1) int get_suffix_link(int location, char c) const { if (location >= 0) location = nodes[location].link[c - MIN_CHAR]; return max(location, 0); } void build(const vector &words) { nodes = {node()}; W = int(words.size()); word_location.resize(W); defer.resize(W); int max_depth = 0; for (int i = 0; i < W; i++) { word_location[i] = add_word(words[i], i); max_depth = max(max_depth, int(words[i].size())); defer[i] = nodes[word_location[i]].word_index; } word_indices_by_depth.resize(W); vector depth_freq(max_depth + 1, 0); for (int i = 0; i < W; i++) depth_freq[words[i].size()]++; for (int i = max_depth - 1; i >= 0; i--) depth_freq[i] += depth_freq[i + 1]; for (int i = 0; i < W; i++) word_indices_by_depth[--depth_freq[words[i].size()]] = i; vector q = {0}; for (int i = 0; i < int(q.size()); i++) { int current = q[i]; for (char c = MIN_CHAR; c < MIN_CHAR + ALPHABET; c++) { int &index = nodes[current][c]; if (index >= 0) { int suffix_parent = get_suffix_link(nodes[current].suff, c); nodes[index].suff = suffix_parent; nodes[index].word_count += nodes[suffix_parent].word_count; nodes[index].dict = nodes[suffix_parent].word_index < 0 ? nodes[suffix_parent].dict : suffix_parent; q.push_back(index); } else { index = get_suffix_link(nodes[current].suff, c); } } } } }; void solve() { ll n, l, r; assert(cin >> n >> l >> r); string temp; assert(!(cin >> temp)); assert(1 <= n and n <= 5000); assert(1 <= l and r <= 1e18); assert(1 <= r and r <= 1e18); assert(l <= r); vector F; ll f = 1, f1 = 1, f2 = 0; while (f <= r) { if (f >= l) F.push_back(to_string(f)); ll temp = f + f1; f2 = f1, f1 = f, f = temp; } if (F.empty()) { cout << modpow(10, n) - 1 << "\n"; return; } AhoCorasick<'0', 10> aho(F); mint dp[5010][1010] = {}; dp[0][0] = 1; rep(i, n) rep(state, aho.nodes.size()) rep(j, 10) { int next_state = aho.get_suffix_link(state, '0' + j); if (aho.nodes[next_state].word_index == -1) dp[i + 1][next_state] += dp[i][state]; } mint sum = 0; rep(state, aho.nodes.size()) sum += dp[n][state]; sum -= 1; cout << sum << "\n"; } int main() { solve(); }