結果
問題 |
No.3089 Base M Numbers, But Only 0~9
|
ユーザー |
|
提出日時 | 2025-04-04 23:03:21 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 22 ms / 2,000 ms |
コード長 | 14,661 bytes |
コンパイル時間 | 2,975 ms |
コンパイル使用メモリ | 199,168 KB |
実行使用メモリ | 11,440 KB |
最終ジャッジ日時 | 2025-04-04 23:03:26 |
合計ジャッジ時間 | 4,040 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge2 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 5 |
other | AC * 19 |
ソースコード
#include <bits/stdc++.h> using namespace std; #define overload4(_1, _2, _3, _4, name, ...) name #define rep1(n) for(int i = 0; i < (int)(n); ++i) #define rep2(i, n) for(int i = 0; i < (int)(n); ++i) #define rep3(i, a, b) for(int i = (a); i < (int)(b); ++i) #define rep4(i, a, b, c) for(int i = (a); i < (int)(b); i += (c)) #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; --i) #define ALL(a) (a).begin(), (a).end() #define Sort(a) (sort((a).begin(), (a).end())) #define RSort(a) (sort((a).rbegin(), (a).rend())) #define UNIQUE(a) (a.erase(unique((a).begin(), (a).end()), (a).end())) typedef long long int ll; typedef unsigned long long ul; typedef long double ld; typedef vector<int> vi; typedef vector<long long> vll; typedef vector<char> vc; typedef vector<string> vst; typedef vector<double> vd; typedef vector<long double> vld; typedef pair<long long, long long> P; template<class T> long long sum(const T &a){ return accumulate(a.begin(), a.end(), 0LL); } template<class T> auto min(const T &a){ return *min_element(a.begin(), a.end()); } template<class T> auto max(const T &a){ return *max_element(a.begin(), a.end()); } const long long MINF = 0x7fffffffffff; const long long INF = 0x1fffffffffffffff; const long long MOD = 998244353; const long double EPS = 1e-9; const long double PI = acos(-1); template<class T> inline bool chmax(T &a, T b) { if(a < b) { a = b; return 1; } return 0; } template<class T> inline bool chmin(T &a, T b) { if(a > b) { a = b; return 1; } return 0; } template<typename T1, typename T2> istream &operator>>(istream &is, pair<T1, T2> &p){ is >> p.first >> p.second; return is; } template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){ os << "(" << p.first << ", " << p.second << ")"; return os; } template<typename T> istream &operator>>(istream &is, vector<T> &v){ for(T &in : v) is >> in; return is; } template<typename T> ostream &operator<<(ostream &os, const vector<T> &v){ for(int i = 0; i < (int) v.size(); ++i){ os << v[i] << (i + 1 != (int) v.size() ? " " : ""); } return os; } template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp){ for(auto &[key, val] : mp){ os << key << ":" << val << " "; } return os; } template <typename T> ostream &operator<<(ostream &os, const set<T> &st){ auto itr = st.begin(); for(int i = 0; i < (int) st.size(); ++i){ os << *itr << (i + 1 != (int) st.size() ? " " : ""); itr++; } return os; } template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st){ auto itr = st.begin(); for(int i = 0; i < (int) st.size(); ++i){ os << *itr << (i + 1 != (int) st.size() ? " " : ""); itr++; } return os; } template <typename T> ostream &operator<<(ostream &os, queue<T> q){ while(q.size()){ os << q.front() << " "; q.pop(); } return os; } template <typename T> ostream &operator<<(ostream &os, deque<T> q){ while(q.size()){ os << q.front() << " "; q.pop_front(); } return os; } template <typename T> ostream &operator<<(ostream &os, stack<T> st){ while(st.size()){ os << st.top() << " "; st.pop(); } return os; } template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq){ while(pq.size()){ os << pq.top() << " "; pq.pop(); } return os; } template <typename T> long long binary_search(long long ok, long long ng, T check){ while(abs(ok - ng) > 1){ long long mid = (ok + ng) / 2; if(check(mid)) ok = mid; else ng = mid; } return ok; } template <typename T> long double binary_search_real(long double ok, long double ng, T check, int iter = 100){ for(int i = 0; i < iter; ++i){ long double mid = (ok + ng) / 2; if(check(mid)) ok = mid; else ng = mid; } return ok; } template <typename T> long long trisum(T a, T b){ long long res = ((b - a + 1) * (a + b)) / 2; return res; } template <typename T> T intpow(T x, int n){ T ret = 1; while(n > 0) { if(n & 1) (ret *= x); (x *= x); n >>= 1; } return ret; } template <typename T> T getReminder(T a, T b){ if(b == 0) return -1; if(a >= 0 && b > 0){ return a % b; } else if(a < 0 && b > 0){ return ((a % b) + b) % b; } else if(a >= 0 && b < 0){ return a % b; } else{ return (abs(b) - abs(a % b)) % b; } } template<class T, class U> inline T vin(T &vec, U n) { vec.resize(n); for(int i = 0; i < (int) n; ++i) cin >> vec[i]; return vec; } template<class T> inline void vout(T vec, string s = "\n"){ for(auto x : vec) cout << x << s; } template<class... T> void in(T&... a){ (cin >> ... >> a); } void out(){ cout << '\n'; } template<class T, class... Ts> void out(const T &a, const Ts&... b){ cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; } template<class T, class U> void inGraph(vector<vector<T>> &G, U n, U m, bool directed = false){ G.resize(n); for(int i = 0; i < m; ++i){ int a, b; cin >> a >> b; a--, b--; G[a].push_back(b); if(!directed) G[b].push_back(a); } } template <long long Modulus> struct ModInt{ long long val; static constexpr int mod() { return Modulus; } constexpr ModInt(const long long _val = 0) noexcept : val(_val) { normalize(); } void normalize(){ val = (val % Modulus + Modulus) % Modulus; } inline ModInt &operator+=(const ModInt &rhs) noexcept { if(val += rhs.val, val >= Modulus) val -= Modulus; return *this; } inline ModInt &operator-=(const ModInt &rhs) noexcept { if(val -= rhs.val, val < 0) val += Modulus; return *this; } inline ModInt &operator*=(const ModInt &rhs) noexcept { val = val * rhs.val % Modulus; return *this; } inline ModInt &operator/=(const ModInt &rhs) noexcept { val = val * inv(rhs.val).val % Modulus; return *this; } inline ModInt &operator++() noexcept { if(++val >= Modulus) val -= Modulus; return *this; } inline ModInt operator++(int) noexcept { ModInt t = val; if(++val >= Modulus) val -= Modulus; return t; } inline ModInt &operator--() noexcept { if(--val < 0) val += Modulus; return *this; } inline ModInt operator--(int) noexcept { ModInt t = val; if(--val < 0) val += Modulus; return t; } inline ModInt operator-() const noexcept { return (Modulus - val) % Modulus; } inline ModInt inv(void) const { return inv(val); } ModInt pow(long long n) const { assert(0 <= n); ModInt x = *this, r = 1; while(n){ if(n & 1) r *= x; x *= x; n >>= 1; } return r; } ModInt inv(const long long n) const { long long a = n, b = Modulus, u = 1, v = 0; while(b){ long long t = a / b; a -= t * b; std::swap(a, b); u -= t * v; std::swap(u, v); } u %= Modulus; if(u < 0) u += Modulus; return u; } friend inline ModInt operator+(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) += rhs; } friend inline ModInt operator-(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) -= rhs; } friend inline ModInt operator*(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) *= rhs; } friend inline ModInt operator/(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) /= rhs; } friend inline bool operator==(const ModInt &lhs, const ModInt &rhs) noexcept { return lhs.val == rhs.val; } friend inline bool operator!=(const ModInt &lhs, const ModInt &rhs) noexcept { return lhs.val != rhs.val; } friend inline std::istream &operator>>(std::istream &is, ModInt &x) noexcept { is >> x.val; x.normalize(); return is; } friend inline std::ostream &operator<<(std::ostream &os, const ModInt &x) noexcept { return os << x.val; } }; using mint = ModInt<MOD>; namespace modcalc{ using i64 = long long; i64 modpow(i64 x, i64 n, const i64 &m){ i64 ret = 1 % m; x %= m; while(n > 0){ if(n & 1) (ret *= x) %= m; (x *= x) %= m; n >>= 1; } return ret; } i64 modinv(i64 a, const i64 m){ i64 b = m, u = 1, v = 0; while(b){ i64 t = a / b; a -= t * b; std::swap(a, b); u -= t * v; std::swap(u, v); } u %= m; if(u < 0) u += m; return u; } i64 modarithmeticsum(i64 a, i64 d, i64 n, const i64 m){ i64 m2 = m * 2; a %= m2, n %= m2, d %= m2; i64 b = (n + m2 - 1) * d % m2; return ((n * (a * 2 + b) % m2) / 2) % m; } i64 modgeometricsum(i64 a, i64 r, i64 n, const i64 m){ a %= m; if(r == 1){ n %= m; return a * n % m; } return a * (modpow(r, n, m) + m - 1) % m * modinv(r - 1, m) % m; } i64 modgeometricsum2(i64 a, i64 r, i64 n, const i64 m){ a %= m; if(r == 1){ n %= m; return a * n % m; } i64 ret = 0; i64 x = 1 % m; i64 sum = 0; for(int i = 0; n > 0; ++i){ if(n & 1){ (ret += x * modpow(r, sum, m) % m) %= m; sum |= 1LL << i; } (x += x * modpow(r, 1LL << i, m) % m) %= m; n >>= 1; } return a * ret % m; } // https://37zigen.com/tonelli-shanks-algorithm/ i64 modsqrt(i64 a, const i64 p){ a %= p; if(a <= 1) return a; // オイラーの規準 if(modpow(a, (p - 1) / 2, p) != 1) return -1; i64 b = 1; while(modpow(b, (p - 1) / 2, p) == 1) b++; // p - 1 = m 2^e i64 m = p - 1, e = 0; while(m % 2 == 0) m >>= 1, e++; // x = a^((m + 1) / 2) (mod p) i64 x = modpow(a, (m - 1) / 2, p); // y = a^{-1} x^2 (mod p) i64 y = a * x % p * x % p; (x *= a) %= p; i64 z = modpow(b, m, p); while(y != 1){ i64 j = 0, t = y; while(t != 1){ (t *= t) %= p; j++; } // e - j ビット目が 1 z = modpow(z, 1LL << (e - j - 1), p); (x *= z) %= p; (z *= z) %= p; (y *= z) %= p; e = j; } return x; } } template <typename T, T (*op)(T, T), T(*e)()> struct SegTree{ int _n, n; std::vector<T> dat; SegTree(int _n) : _n(_n) { int x = 1; while(_n > x){ x *= 2; } n = x; dat.resize(n * 2); for(int i = 0; i < n * 2; ++i){ dat[i] = e(); } } SegTree(std::vector<T> &v) : _n((int) v.size()) { int x = 1; while((int) v.size() > x){ x *= 2; } n = x; dat.resize(n * 2); for(int i = 0; i < n; ++i){ set(i, (i < (int) v.size() ? v[i] : e())); } build(); } private: void set(int i, const T &x){ dat[i + n] = x; } void build(){ for(int k = n - 1; k >= 1; k--) dat[k] = op(dat[k * 2], dat[k * 2 + 1]); } public: T get(int i) const { assert(0 <= i && i < n); return dat[i + n]; } void update(int i, const T &x){ assert(0 <= i && i < n); i += n; dat[i] = x; while(i > 0){ i >>= 1; // parent dat[i] = op(dat[i * 2], dat[i * 2 + 1]); } } T query(int a, int b){ assert(0 <= a && a <= b && b <= n); T vl = e(); T vr = e(); int l = a + n; int r = b + n; while(l < r){ if(l & 1) vl = op(vl, dat[l++]); if(r & 1) vr = op(dat[--r], vr); l >>= 1; r >>= 1; } return op(vl, vr); } template <class F> int max_right(int l, F f) const { assert(0 <= l && l <= _n); assert(f(e())); if(l == _n) return _n; l += n; T sm = e(); do{ while(l % 2 == 0) l >>= 1; if(!f(op(sm, dat[l]))){ while(l < n){ l = (2 * l); if(f(op(sm, dat[l]))){ sm = op(sm, dat[l]); l++; } } return l - n; } sm = op(sm, dat[l]); l++; }while((l & -l) != l); return _n; } template <class F> int min_left(int r, F f) const { assert(0 <= r && r <= _n); assert(f(e())); if(r == 0) return 0; r += n; T sm = e(); do{ r--; while(r > 1 && (r % 2)) r >>= 1; if(!f(op(dat[r], sm))){ while(r < n){ r = (2 * r + 1); if(f(op(dat[r], sm))){ sm = op(dat[r], sm); r--; } } return r + 1 - n; } sm = op(dat[r], sm); }while((r & -r) != r); return 0; } }; mint op(mint a, mint b){ return a * b; } mint e(){ return 1; } ll T; void input(){ in(T); } mint dp1[200001][2], dp2[200001][2]; void solve(){ ll m; in(m); string n; in(n); ll len = n.size(); mint mm = m; vector<mint> base(len + 1, 1); rep(i, 1, len + 1) base[i] = base[i - 1] * mm; dp1[0][0] = 1; dp2[0][0] = 0; rep(i, len){ ll d = n[i] - '0'; if(d == 0){ ll cnt = m / 10 + (d < m % 10); mint s = modcalc::modarithmeticsum(d, 10LL, cnt, MOD); dp1[i + 1][1] += dp1[i][0] * (cnt - 1) + dp1[i][1] * cnt; dp2[i + 1][1] += dp2[i][0] * (cnt - 1) + s * base[len - 1 - i] * dp1[i][0]; dp2[i + 1][1] += dp2[i][1] * cnt + s * base[len - 1 - i] * dp1[i][1]; }else{ ll cnt = m / 10 + (d < m % 10); mint s = modcalc::modarithmeticsum(d, 10LL, cnt, MOD); dp1[i + 1][1] += (dp1[i][0] + dp1[i][1]) * cnt; dp2[i + 1][1] += dp2[i][0] * cnt + s * base[len - 1 - i] * dp1[i][0]; dp2[i + 1][1] += dp2[i][1] * cnt + s * base[len - 1 - i] * dp1[i][1]; } } out(dp2[len][1]); } int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(20); T = 1; // input(); while(T--) solve(); }