結果
| 問題 |
No.3089 Base M Numbers, But Only 0~9
|
| ユーザー |
 dyktr_06
|
| 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 |
（要ログイン）
| 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();
}