結果
| 問題 |
No.2589 Prepare Integers
|
| コンテスト | |
| ユーザー |
 hos.lyric
|
| 提出日時 | 2023-12-17 00:54:46 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 66 ms / 2,000 ms |
| コード長 | 11,422 bytes |
| コンパイル時間 | 1,201 ms |
| コンパイル使用メモリ | 119,360 KB |
| 実行使用メモリ | 6,944 KB |
| 最終ジャッジ日時 | 2024-09-27 07:53:24 |
| 合計ジャッジ時間 | 2,497 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge3 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 24 |
ソースコード
#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using Int = long long;
template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")
////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
static constexpr unsigned M = M_;
unsigned x;
constexpr ModInt() : x(0U) {}
constexpr ModInt(unsigned x_) : x(x_ % M) {}
constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
ModInt pow(long long e) const {
if (e < 0) return inv().pow(-e);
ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
}
ModInt inv() const {
unsigned a = M, b = x; int y = 0, z = 1;
for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
assert(a == 1U); return ModInt(y);
}
ModInt operator+() const { return *this; }
ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
explicit operator bool() const { return x; }
bool operator==(const ModInt &a) const { return (x == a.x); }
bool operator!=(const ModInt &a) const { return (x != a.x); }
friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////
constexpr unsigned MO = 998244353;
using Mint = ModInt<MO>;
#define ModInt ModIntRunTime
////////////////////////////////////////////////////////////////////////////////
struct ModInt {
static unsigned M;
unsigned x;
ModInt() : x(0U) {}
ModInt(unsigned x_) : x(x_ % M) {}
ModInt(unsigned long long x_) : x(x_ % M) {}
ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
ModInt pow(long long e) const {
if (e < 0) return inv().pow(-e);
ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
}
ModInt inv() const {
unsigned a = M, b = x; int y = 0, z = 1;
for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
assert(a == 1U); return ModInt(y);
}
ModInt operator+() const { return *this; }
ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
explicit operator bool() const { return x; }
bool operator==(const ModInt &a) const { return (x == a.x); }
bool operator!=(const ModInt &a) const { return (x != a.x); }
friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
unsigned ModInt::M;
////////////////////////////////////////////////////////////////////////////////
#undef ModInt
// a x + b y = g
int gojo(int a, int b, int &x, int &y) {
if (b) {
const int g = gojo(b, a % b, y, x);
y -= (a / b) * x;
return g;
} else {
x = 1;
y = 0;
return a;
}
}
int D, M;
// generating <a[0], ..., a[D - 1]>
// a: upper triangular
// a[i][i] = 0 or a[i][i] | M
constexpr int MAX_D = 110;
ModIntRunTime a[MAX_D][MAX_D];
void init() {
for (int i = 0; i < D; ++i) {
fill(a[i], a[i] + D, 0);
}
}
void add(vector<ModIntRunTime> bs) { // call by value
for (int i = 0; i < D; ++i) if (bs[i].x) {
const int a0 = a[i][i].x ? a[i][i].x : M;
int x, y;
const int g = gojo(a0, bs[i].x, x, y);
const int z = -(int)bs[i].x / g, w = a0 / g;
// [ g ] = [ x y ] [ a ]
// [ 0 ] [ z w ] [ b ]
a[i][i] = g;
for (int j = i + 1; j < D; ++j) {
const ModIntRunTime t = x * a[i][j] + y * bs[j];
bs[j] = z * a[i][j] + w * bs[j];
a[i][j] = t;
}
}
}
bool check(vector<ModIntRunTime> bs) { // call by value
for (int i = 0; i < D; ++i) if (bs[i]) {
if (!a[i][i].x || bs[i].x % a[i][i].x != 0) {
return false;
}
const int x = bs[i].x / a[i][i].x;
for (int j = i + 1; j < D; ++j) {
bs[j] -= x * a[i][j];
}
}
return true;
}
vector<ModIntRunTime> lexMax() {
vector<ModIntRunTime> bs(D, 0);
for (int i = 0; i < D; ++i) if (a[i][i].x) {
const int x = (M - 1 - bs[i].x) / a[i][i].x;
for (int j = i; j < D; ++j) {
bs[j] += x * a[i][j];
}
}
return bs;
}
template <class T> T count() {
T prod = 1;
for (int i = 0; i < D; ++i) if (a[i][i].x) {
prod *= (M / a[i][i].x);
}
return prod;
}
int main() {
int Q;
for (; ~scanf("%d%d", &M, &Q); ) {
ModIntRunTime::M = M;
D = 0;
for (Int x = 1001001001LL; x; x /= M) ++D;
cerr<<"M = "<<M<<", D = "<<D<<endl;
init();
for (int q = 0; q < Q; ++q) {
// for(int i=0;i<D;++i)if(a[i][i].x){cerr<<i<<": ";pv(a[i],a[i]+D);}
int typ;
scanf("%d", &typ);
switch (typ) {
case 1: {
Int X;
scanf("%lld", &X);
vector<ModIntRunTime> V(D);
for (int i = 0; i < D; ++i) {
V[i] = X;
X /= M;
}
assert(!X);
reverse(V.begin(), V.end());
// cerr<<COLOR("33")<<"add "<<V<<COLOR()<<endl;
add(V);
} break;
case 2: {
Int K;
scanf("%lld", &K);
--K;
// cerr<<COLOR("33")<<"kth "<<K<<COLOR()<<endl;
vector<Int> prods(D + 1);
prods[D] = 1;
for (int i = D; --i >= 0; ) {
prods[i] = (a[i][i].x ? (M / a[i][i].x) : 1) * prods[i + 1];
}
if (K < prods[0]) {
vector<ModIntRunTime> V(D, 0);
Int k = K;
for (int i = 0; i < D; ++i) if (a[i][i].x) {
const Int r = k / prods[i + 1];
k %= prods[i + 1];
const Int s = -((Int)V[i].x / (Int)a[i][i].x) + r;
for (int j = i; j < D; ++j) {
V[j] += s * a[i][j];
}
}
Int ans = 0;
for (int i = 0; i < D; ++i) {
(ans *= M) += V[i].x;
}
printf("%lld\n", ans);
} else {
puts("-1");
}
} break;
case 3: {
Int X;
scanf("%lld", &X);
++X;
vector<ModIntRunTime> V(D);
for (int i = 0; i < D; ++i) {
V[i] = X;
X /= M;
}
reverse(V.begin(), V.end());
// cerr<<COLOR("33")<<"rank "<<X<<" "<<V<<COLOR()<<endl;
vector<Int> prods(D + 1);
prods[D] = 1;
for (int i = D; --i >= 0; ) {
prods[i] = (a[i][i].x ? (M / a[i][i].x) : 1) * prods[i + 1];
}
Int ans = 0;
if (X) {
ans += prods[0];
} else {
vector<ModIntRunTime> W(D, 0);
for (int i = 0; i < D; ++i) {
if (a[i][i].x) {
const Int w = (Int)W[i].x % (Int)a[i][i].x;
if (w <= V[i].x) {
const Int q = (Int)(V[i].x - w) / (Int)a[i][i].x;
const Int r = (Int)(V[i].x - w) % (Int)a[i][i].x;
// cerr<<" W = "<<W<<", i = "<<i<<", w = "<<w<<", q = "<<q<<", r = "<<r<<endl;
if (r) {
ans += (q + 1) * prods[i + 1];
break;
} else {
ans += q * prods[i + 1];
const Int s = -((Int)W[i].x / (Int)a[i][i].x) + q;
for (int j = i; j < D; ++j) {
W[j] += s * a[i][j];
}
}
} else {
break;
}
} else {
const Int w = (Int)W[i].x;
if (w < V[i].x) {
ans += prods[i + 1];
break;
} else if (w == V[i].x) {
//
} else {
break;
}
}
}
}
printf("%lld\n", ans);
} break;
default: assert(false);
}
}
cerr<<string(80,'=')<<endl;
}
return 0;
}