結果

問題 No.1261 数字集め
ユーザー hitonanodehitonanode
提出日時 2020-10-16 23:32:43
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 17,044 bytes
コンパイル時間 4,162 ms
コンパイル使用メモリ 248,500 KB
最終ジャッジ日時 2025-01-15 09:49:55
ジャッジサーバーID
(参考情報)
judge2 / judge3
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ファイルパターン 結果
other AC * 43 WA * 51
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ソースコード

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プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each
    (begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }
template <typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l
    .second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l
    .second - r.second); }
template <typename T> vector<T> srtunq(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return
    vec; }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return
    is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { std::apply([&os](auto &&... args) { ((os << args << ','), ...);},
    tpl); return os; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os;
    }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ',';
    os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os;
    }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}';
    return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')';
    return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v
    .second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp)
    os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl
#else
#define dbg(x) {}
#endif
template <int mod>
struct ModInt
{
using lint = long long;
static int get_mod() { return mod; }
static int get_primitive_root() {
static int primitive_root = 0;
if (!primitive_root) {
primitive_root = [&](){
std::set<int> fac;
int v = mod - 1;
for (lint i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i;
if (v > 1) fac.insert(v);
for (int g = 1; g < mod; g++) {
bool ok = true;
for (auto i : fac) if (ModInt(g).power((mod - 1) / i) == 1) { ok = false; break; }
if (ok) return g;
}
return -1;
}();
}
return primitive_root;
}
int val;
constexpr ModInt() : val(0) {}
constexpr ModInt &_setval(lint v) { val = (v >= mod ? v - mod : v); return *this; }
constexpr ModInt(lint v) { _setval(v % mod + mod); }
explicit operator bool() const { return val != 0; }
constexpr ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); }
constexpr ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + mod); }
constexpr ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % mod); }
constexpr ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % mod); }
constexpr ModInt operator-() const { return ModInt()._setval(mod - val); }
constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % mod + x.val); }
friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % mod - x.val + mod); }
friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.val % mod); }
friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.inv() % mod); }
constexpr bool operator==(const ModInt &x) const { return val == x.val; }
constexpr bool operator!=(const ModInt &x) const { return val != x.val; }
bool operator<(const ModInt &x) const { return val < x.val; } // To use std::map<ModInt, T>
friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; is >> t; x = ModInt(t); return is; }
friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { os << x.val; return os; }
constexpr lint power(lint n) const {
lint ans = 1, tmp = this->val;
while (n) {
if (n & 1) ans = ans * tmp % mod;
tmp = tmp * tmp % mod;
n /= 2;
}
return ans;
}
constexpr ModInt pow(lint n) const {
return power(n);
}
constexpr lint inv() const { return this->power(mod - 2); }
constexpr ModInt operator^(lint n) const { return ModInt(this->power(n)); }
constexpr ModInt &operator^=(lint n) { return *this = *this ^ n; }
inline ModInt fac() const {
static std::vector<ModInt> facs;
int l0 = facs.size();
if (l0 > this->val) return facs[this->val];
facs.resize(this->val + 1);
for (int i = l0; i <= this->val; i++) facs[i] = (i == 0 ? ModInt(1) : facs[i - 1] * ModInt(i));
return facs[this->val];
}
ModInt doublefac() const {
lint k = (this->val + 1) / 2;
if (this->val & 1) return ModInt(k * 2).fac() / ModInt(2).power(k) / ModInt(k).fac();
else return ModInt(k).fac() * ModInt(2).power(k);
}
ModInt nCr(const ModInt &r) const {
if (this->val < r.val) return ModInt(0);
return this->fac() / ((*this - r).fac() * r.fac());
}
ModInt sqrt() const {
if (val == 0) return 0;
if (mod == 2) return val;
if (power((mod - 1) / 2) != 1) return 0;
ModInt b = 1;
while (b.power((mod - 1) / 2) == 1) b += 1;
int e = 0, m = mod - 1;
while (m % 2 == 0) m >>= 1, e++;
ModInt x = power((m - 1) / 2), y = (*this) * x * x;
x *= (*this);
ModInt z = b.power(m);
while (y != 1) {
int j = 0;
ModInt t = y;
while (t != 1) j++, t *= t;
z = z.power(1LL << (e - j - 1));
x *= z, z *= z, y *= z;
e = j;
}
return ModInt(std::min(x.val, mod - x.val));
}
};
using mint = ModInt<1000000007>;
// Sieve of Eratosthenes
// (*this)[i] = (divisor of i, greater than 1)
// Example: [0, 1, 2, 3, 2, 5, 3, 7, 2, 3, 2, 11, ...]
// Complexity: Space O(MAXN), Time (construction) O(MAXNloglogMAXN)
struct SieveOfEratosthenes : std::vector<int>
{
std::vector<int> primes;
SieveOfEratosthenes(int MAXN) : std::vector<int>(MAXN + 1) {
std::iota(begin(), end(), 0);
for (int i = 2; i <= MAXN; i++) {
if ((*this)[i] == i) {
primes.push_back(i);
for (int j = i; j <= MAXN; j += i) (*this)[j] = i;
}
}
}
using T = long long int;
// Prime factorization for x <= MAXN^2
// Complexity: O(log x) (x <= MAXN)
// O(MAXN / logMAXN) (MAXN < x <= MAXN^2)
std::map<T, int> Factorize(T x) {
assert(x <= 1LL * (int(size()) - 1) * (int(size()) - 1));
std::map<T, int> ret;
if (x < int(size())) {
while (x > 1) {
ret[(*this)[x]]++;
x /= (*this)[x];
}
}
else {
for (auto p : primes) {
while (!(x % p)) x /= p, ret[p]++;
if (x == 1) break;
}
if (x > 1) ret[x]++;
}
return ret;
}
std::vector<T> Divisors(T x) {
std::vector<T> ret{1};
for (auto p : Factorize(x)) {
int n = ret.size();
for (int i = 0; i < n; i++) {
for (T a = 1, d = 1; d <= p.second; d++) {
a *= p.first;
ret.push_back(ret[i] * a);
}
}
}
return ret; // Not sorted
}
// Moebius function Table
// return: [0=>0, 1=>1, 2=>-1, 3=>-1, 4=>0, 5=>-1, 6=>1, 7=>-1, 8=>0, ...]
std::vector<int> GenerateMoebiusFunctionTable() {
std::vector<int> ret(size());
for (int i = 1; i < int(size()); i++) {
if (i == 1) ret[i] = 1;
else if ((i / (*this)[i]) % (*this)[i] == 0) ret[i] = 0;
else ret[i] = -ret[i / (*this)[i]];
}
return ret;
}
};
SieveOfEratosthenes sieve(1000000);
// Integer convolution for arbitrary mod
// with NTT (and Garner's algorithm) for ModInt / ModIntRuntime class.
// We skip Garner's algorithm if `skip_garner` is true or mod is in `nttprimes`.
// input: a (size: n), b (size: m)
// return: vector (size: n + m - 1)
template <typename MODINT>
std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner = false);
constexpr int nttprimes[3] = {998244353, 167772161, 469762049};
// Integer FFT (Fast Fourier Transform) for ModInt class
// (Also known as Number Theoretic Transform, NTT)
// is_inverse: inverse transform
// ** Input size must be 2^n **
template <typename MODINT>
void ntt(std::vector<MODINT> &a, bool is_inverse = false)
{
int n = a.size();
if (n == 1) return;
static const int mod = MODINT::get_mod();
static const MODINT root = MODINT::get_primitive_root();
assert(__builtin_popcount(n) == 1 and (mod - 1) % n == 0);
static std::vector<MODINT> w{1}, iw{1};
for (int m = w.size(); m < n / 2; m *= 2) {
MODINT dw = root.power((mod - 1) / (4 * m)), dwinv = 1 / dw;
w.resize(m * 2), iw.resize(m * 2);
for (int i = 0; i < m; i++) w[m + i] = w[i] * dw, iw[m + i] = iw[i] * dwinv;
}
if (!is_inverse) {
for (int m = n; m >>= 1;) {
for (int s = 0, k = 0; s < n; s += 2 * m, k++) {
for (int i = s; i < s + m; i++) {
MODINT x = a[i], y = a[i + m] * w[k];
a[i] = x + y, a[i + m] = x - y;
}
}
}
}
else {
for (int m = 1; m < n; m *= 2) {
for (int s = 0, k = 0; s < n; s += 2 * m, k++) {
for (int i = s; i < s + m; i++) {
MODINT x = a[i], y = a[i + m];
a[i] = x + y, a[i + m] = (x - y) * iw[k];
}
}
}
int n_inv = MODINT(n).inv();
for (auto &v : a) v *= n_inv;
}
}
template <int MOD>
std::vector<ModInt<MOD>> nttconv_(const std::vector<int> &a, const std::vector<int> &b) {
int sz = a.size();
assert(a.size() == b.size() and __builtin_popcount(sz) == 1);
std::vector<ModInt<MOD>> ap(sz), bp(sz);
for (int i = 0; i < sz; i++) ap[i] = a[i], bp[i] = b[i];
ntt(ap, false);
if (a == b) bp = ap;
else ntt(bp, false);
for (int i = 0; i < sz; i++) ap[i] *= bp[i];
ntt(ap, true);
return ap;
}
long long garner_ntt_(int r0, int r1, int r2, int mod)
{
using mint2 = ModInt<nttprimes[2]>;
static const long long m01 = 1LL * nttprimes[0] * nttprimes[1];
static const long long m0_inv_m1 = ModInt<nttprimes[1]>(nttprimes[0]).inv();
static const long long m01_inv_m2 = mint2(m01).inv();
int v1 = (m0_inv_m1 * (r1 + nttprimes[1] - r0)) % nttprimes[1];
auto v2 = (mint2(r2) - r0 - mint2(nttprimes[0]) * v1) * m01_inv_m2;
return (r0 + 1LL * nttprimes[0] * v1 + m01 % mod * v2.val) % mod;
}
template <typename MODINT>
std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner)
{
int sz = 1, n = a.size(), m = b.size();
while (sz < n + m) sz <<= 1;
if (sz <= 16) {
std::vector<MODINT> ret(n + m - 1);
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) ret[i + j] += a[i] * b[j];
}
return ret;
}
int mod = MODINT::get_mod();
if (skip_garner or std::find(std::begin(nttprimes), std::end(nttprimes), mod) != std::end(nttprimes))
{
a.resize(sz), b.resize(sz);
if (a == b) { ntt(a, false); b = a; }
else ntt(a, false), ntt(b, false);
for (int i = 0; i < sz; i++) a[i] *= b[i];
ntt(a, true);
a.resize(n + m - 1);
}
else {
std::vector<int> ai(sz), bi(sz);
for (int i = 0; i < n; i++) ai[i] = a[i].val;
for (int i = 0; i < m; i++) bi[i] = b[i].val;
auto ntt0 = nttconv_<nttprimes[0]>(ai, bi);
auto ntt1 = nttconv_<nttprimes[1]>(ai, bi);
auto ntt2 = nttconv_<nttprimes[2]>(ai, bi);
a.resize(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
a[i] = garner_ntt_(ntt0[i].val, ntt1[i].val, ntt2[i].val, mod);
}
}
return a;
}
// Calculate [x^N](num(x) / den(x))
// Coplexity: O(LlgLlgN) ( L = size(num) + size(den) )
template <typename Tp>
Tp coefficient_of_rational_function(long long N, std::vector<Tp> num, std::vector<Tp> den)
{
assert(N >= 0);
while (den.size() and den.back() == 0) den.pop_back();
assert(den.size());
int h = 0;
while (den[h] == 0) h++;
N += h;
den.erase(den.begin(), den.begin() + h);
if (den.size() == 1)
{
assert(N < int(num.size()));
return num[N] / den[0];
}
while (N)
{
std::vector<Tp> g = den;
for (size_t i = 1; i < g.size(); i += 2)
{
g[i] = -g[i];
}
auto conv_num_g = nttconv(num, g);
num.resize((conv_num_g.size() + 1 - (N & 1)) / 2);
for (size_t i = 0; i < num.size(); i++)
{
num[i] = conv_num_g[i * 2 + (N & 1)];
}
auto conv_den_g = nttconv(den, g);
for (size_t i = 0; i < den.size(); i++)
{
den[i] = conv_den_g[i * 2];
}
N >>= 1;
}
return num[0] / den[0];
}
int main()
{
int N, M;
cin >> N >> M;
vector<mint> A(N + 1);
FOR(i, 2, N + 1) cin >> A[i];
vector<lint> nd = sieve.Divisors(N);
mint ret = 0;
auto add = [&](int x, int y) -> void {
// 1 -> x -> y -> N
vector<mint> num { 1 };
auto den = nttconv<mint>(nttconv<mint>(vector<mint> { 1, -A[x] + 1 }, vector<mint> { 1, -A[y] + 1 }), vector<mint> { 1, -A[N] + 1 });
mint tmp = coefficient_of_rational_function<mint>(M - 3, num, den);
ret += tmp;
};
for (auto x : nd) if (x > 1) for (auto y : nd) if (y > x and y < N and y % x == 0)
{
add(x, y);
}
cout << ret << '\n';
int Q;
cin >> Q;
vector<set<int>> prv(N + 1), nxt(N + 1);
for (auto x : nd) for (auto y : nd) if (y > x and y % x == 0 and x > 1) prv[y].insert(x), nxt[x].insert(y);
while (Q--) {
int x, y;
cin >> x >> y;
prv[y].insert(x), nxt[x].insert(y);
if (y == N) {
for (auto xx : prv[x]) {
add(xx, x);
}
} else {
if (prv[N].count(y)) {
add(x, y);
}
}
cout << ret << '\n';
}
}
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