結果
| 問題 |
No.3089 Base M Numbers, But Only 0~9
|
| コンテスト | |
| ユーザー |
 hint908
|
| 提出日時 | 2025-04-30 13:19:28 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 114 ms / 2,000 ms |
| コード長 | 6,459 bytes |
| コンパイル時間 | 4,071 ms |
| コンパイル使用メモリ | 296,696 KB |
| 実行使用メモリ | 9,088 KB |
| 最終ジャッジ日時 | 2025-04-30 13:19:36 |
| 合計ジャッジ時間 | 7,789 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge1 |
（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
// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
#include<bits/stdc++.h>
using namespace std;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
template<class T> using V = vector<T>;
template<class T> using VV = V<V<T>>;
template<class T> using VVV = V<VV<T>>;
template<class T> using VVVV = VV<VV<T>>;
#define rep(i,n) for(ll i=0ll;(i)<(n);(i)++)
#define REP(i,a,n) for(ll i=(a);(i)<(n);(i)++)
#define rrep(i,n) for(ll i=(n)-1;(i)>=(0ll);(i)--)
#define RREP(i,a,n) for(ll i=(n)-1;(i)>=(a);(i)--)
const long long INF = (1LL << 60);
const long long mod99 = 998244353;
const long long mod107 = 1000000007;
const long long mod = mod99;
#define eb emplace_back
#define be(v) (v).begin(),(v).end()
#define all(v) (v).begin(),(v).end()
#define foa(i,v) for(auto& (i) : (v))
#define UQ(v) sort(be(v)), (v).erase(unique(be(v)), (v).end())
#define UQ2(v,cmp) sort(be(v)), (v).erase(unique(be(v),cmp), (v).end())
#define UQ3(v,cmp) sort(be(v),cmp), (v).erase(unique(be(v)), (v).end())
#define UQ4(v,cmp,cmp2) sort(be(v), cmp), (v).erase(unique(be(v),cmp2), (v).end())
#define LB(x,v) (lower_bound(be(v),(x))-(v).begin())
#define LB2(x,v,cmp) (lower_bound(be(v),(x),(cmp))-(v).begin())
#define UB(x,v) (upper_bound(be(v),(x))-(v).begin())
#define UB2(x,v,cmp) (upper_bound(be(v),(x),(cmp))-(v).begin())
#define dout() cout << fixed << setprecision(20)
#define randinit() srand((unsigned)time(NULL))
template<class T, class U> bool chmin(T& t, const U& u) { if (t > u){ t = u; return 1;} return 0; }
template<class T, class U> bool chmax(T& t, const U& u) { if (t < u){ t = u; return 1;} return 0; }
ll Rnd(ll L=0, ll R=mod99){return rand()%(R-L)+L;}
VV<ll> matmul(VV<ll> v, VV<ll> w, ll p=(1ll<<60)){
ll n1 = v.size();
ll n2 = w.size();
ll n3 = w[0].size();
VV<ll> ret(n1, V<ll>(n3, 0));
rep(i, n1) rep(j,n2) rep(k,n3) (ret[i][k] += v[i][j]*w[j][k]) %= p;
return ret;
}
VV<ll> matpow(VV<ll> v, ll k, ll p){
if(k == 1) return v;
ll n = v.size();
VV<ll> ret(n, V<ll>(n, 0));
rep(i, n) ret[i][i] = 1;
if(k == 0) return ret;
VV<ll> w = matpow(v, k/2, p);
w = matmul(w, w, p);
if(k%2) w = matmul(w, v, p);
return w;
}
struct Combination{
vector<long long> fac, inv, finv;
long long MOD;
Combination(long long N = 200100, long long p = 998244353) : fac(N, 1), inv(N, 1), finv(N, 1), MOD(p){
for(long long i = 2; i < N; i++){
fac[i] = fac[i-1] * i % MOD;
inv[i] = MOD - inv[MOD%i] * (MOD/i) % MOD;
finv[i] = finv[i-1] * inv[i] % MOD;
}
}
long long com(long long n, long long k){
if(n < k) return 0;
if(n < 0 || k < 0) return 0;
return fac[n] * finv[k] % MOD * finv[n-k] % MOD;
}
long long per(long long n, long long k){
if(n < k) return 0;
if(n < 0 || k < 0) return 0;
return fac[n] * finv[n-k] % MOD;
}
};
long long modpow(long long n, long long k, long long p = mod){
long long a = n % p;
long long ans = 1;
while(k != 0) {
if(k & 1) ans = ans * a % p;
k /= 2;
a = a * a % p;
}
return ans;
}
// n^(-1) ≡ b (mod p) となる b を求める
long long modinv(long long n, long long p = mod) {
// if(n == 1) return 1;
// return p - modinv(p % n) * (p / n) % p;
return modpow(n, p - 2, p);
}
// n^k ≡ b (mod p) となる最小の k を求める
long long modlog(long long n, long long b, long long p = mod){
long long sqrt_p = sqrt(p);
unordered_map<long long , long long> n_pow;
long long memo = 1;
for(long long i = 0; i < sqrt_p; i ++){
if(!n_pow.count(memo)) n_pow[memo] = i;
memo = memo * n % p;
}
memo = modinv(memo, p);
long long ans = 0;
while(!n_pow.count(b)){
if(ans >= p) return -1;
ans += sqrt_p;
b = b * memo % p;
}
ans += n_pow[b];
return ans % (p - 1);
}
// ax + by = gcd(a, b) を満たす (x, y) が格納される
long long ext_gcd(long long a, long long b, long long &x, long long &y){
if(b == 0){
x = 1;
y = 0;
return a;
}
long long d = ext_gcd(b, a%b, y, x);
y -= a/b*x;
return d;
}
template <typename T, T (*OP)(T, T), T (*E)()>
struct SegmentTree {
vector<T> seg;
ll seg_size;//葉の数
SegmentTree(ll N) : seg(4*N, E()), seg_size() {
seg_size = 1;
while(seg_size < N) seg_size *= 2;
}
SegmentTree(const vector<T> a) : seg(4*a.size(), E()), seg_size() {
ll N = a.size();
seg_size = 1;
while(seg_size < N) seg_size *= 2;
rep(i,N) seg[i + seg_size - 1] = a[i];
for(ll i = seg_size-2; i >= 0; i --){
seg[i] = OP(seg[2*i + 1], seg[2*i + 2]);
}
}
void set(ll idx, T x){
idx += seg_size - 1;
seg[idx] = x;
while(idx > 0){
idx = (idx - 1) / 2;
seg[idx] = OP(seg[2*idx + 1], seg[2*idx + 2]);
}
}
void apply(ll idx, T x){
idx += seg_size - 1;
seg[idx] = OP(seg[idx], x);
while(idx > 0){
idx = (idx - 1) / 2;
seg[idx] = OP(seg[2*idx + 1], seg[2*idx + 2]);
}
}
T prod(ll a, ll b) { return prod_sub(a, b, 0, 0, seg_size); }
T prod_sub(ll a, ll b, ll idx, ll left, ll right){
if(a >= right || b <= left) return E();
if(a <= left && b >= right) return seg[idx];
T v1 = prod_sub(a, b, 2 * idx + 1, left, (left + right) / 2);
T v2 = prod_sub(a, b, 2 * idx + 2, (left + right) / 2, right);
return OP(v1, v2);
}
};
#include<atcoder/modint>
using namespace atcoder;
using mint = modint998244353;
mint e(){return 1;}
mint op(mint l, mint r){return l*r;}
void solve(){
ll m;
string n;
cin >> m >> n;
ll x = n.size();
V<mint> v(x);
V<mint> w(x);
rep(i, x){
ll c = n[i] - '0';
if(c < m%10) v[i] = (m+9)/10;
else v[i] = m/10;
w[i] = v[i];
if(c == 0 and i == 0) v[i]--;
}
SegmentTree<mint, op, e> seg(v);
swap(v, w);
mint ans = 0;
rep(i, x){
ll c = n[i] - '0';
ans += (v[i]*c + v[i]*(v[i]-1)/2*10) * modpow(m, x-i-1) * seg.prod(0,i) * seg.prod(i+1, x);
// cout << ans.val() << endl;
}
cout << ans.val() << endl;
}
int main(){
cin.tie(nullptr);
ios::sync_with_stdio(false);
int t=1;
// cin >> t;
rep(i,t) solve();
}