結果
| 問題 | No.8046 yukicoderの過去問 |
| ユーザー |
👑  emthrm
|
| 提出日時 | 2020-02-18 21:58:23 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
CE
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 18,389 bytes |
| コンパイル時間 | 2,153 ms |
| コンパイル使用メモリ | 205,296 KB |
| 最終ジャッジ日時 | 2024-11-14 22:07:32 |
| 合計ジャッジ時間 | 2,562 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
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コンパイルエラー時のメッセージ・ソースコードは、提出者また管理者しか表示できないようにしております。（リジャッジ後のコンパイルエラーは公開されます）
ただし、clay言語の場合は開発者のデバッグのため、公開されます。
ただし、clay言語の場合は開発者のデバッグのため、公開されます。
コンパイルメッセージ
main.cpp:115:57: error: redefinition of 'template<class T> std::function<std::vector<_Tp>(const std::vector<_Tp>&, const std::vector<_Tp>&)> mul'
115 | function<vector<T>(const vector<T>&, const vector<T>&)> mul = [](const vector<T> &a, const vector<T> &b) {
| ^~~
main.cpp:101:57: note: 'template<class T> std::function<std::vector<_Tp>(const std::vector<_Tp>&, const std::vector<_Tp>&)> mul<T>' previously declared here
101 | function<vector<T>(const vector<T>&, const vector<T>&)> mul = [](const vector<T> &a, const vector<T> &b) {
| ^~~
main.cpp:123:30: error: redefinition of 'template<class T> std::function<bool(const T&, T&)> sqr'
123 | function<bool(const T&, T&)> sqr = [](const T &a, T &res) {
| ^~~
main.cpp:109:30: note: 'template<class T> std::function<bool(const T&, T&)> sqr<T>' previously declared here
109 | function<bool(const T&, T&)> sqr = [](const T &a, T &res) {
| ^~~
ソースコード
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
template <typename T> using posteriority_queue = priority_queue<T, vector<T>, greater<T> >;
const int INF = 0x3f3f3f3f;
const ll LINF = 0x3f3f3f3f3f3f3f3fLL;
const double EPS = 1e-8;
const int MOD = 1000000007;
// const int MOD = 998244353;
const int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};
const int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U> inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U> inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; }
template <typename T> void unique(vector<T> &a) { a.erase(unique(ALL(a)), a.end()); }
struct IOSetup {
IOSetup() {
cin.tie(nullptr);
ios_base::sync_with_stdio(false);
cout << fixed << setprecision(20);
}
} iosetup;
int mod = MOD;
struct ModInt {
unsigned val;
ModInt(): val(0) {}
ModInt(ll x) : val(x >= 0 ? x % mod : x % mod + mod) {}
ModInt pow(ll exponent) {
ModInt tmp = *this, res = 1;
while (exponent > 0) {
if (exponent & 1) res *= tmp;
tmp *= tmp;
exponent >>= 1;
}
return res;
}
ModInt &operator+=(const ModInt &x) { if((val += x.val) >= mod) val -= mod; return *this; }
ModInt &operator-=(const ModInt &x) { if((val += mod - x.val) >= mod) val -= mod; return *this; }
ModInt &operator*=(const ModInt &x) { val = static_cast<unsigned long long>(val) * x.val % mod; return *this; }
ModInt &operator/=(const ModInt &x) {
// assert(__gcd(static_cast<int>(x.val), mod) == 1);
unsigned a = x.val, b = mod; int u = 1, v = 0;
while (b) {
unsigned tmp = a / b;
swap(a -= tmp * b, b);
swap(u -= tmp * v, v);
}
return *this *= u;
}
bool operator==(const ModInt &x) const { return val == x.val; }
bool operator!=(const ModInt &x) const { return val != x.val; }
bool operator<(const ModInt &x) const { return val < x.val; }
bool operator<=(const ModInt &x) const { return val <= x.val; }
bool operator>(const ModInt &x) const { return val > x.val; }
bool operator>=(const ModInt &x) const { return val >= x.val; }
ModInt &operator++() { if (++val == mod) val = 0; return *this; }
ModInt operator++(int) { ModInt res = *this; ++*this; return res; }
ModInt &operator--() { val = (val == 0 ? mod : val) - 1; return *this; }
ModInt operator--(int) { ModInt res = *this; --*this; return res; }
ModInt operator+() const { return *this; }
ModInt operator-() const { return ModInt(val ? mod - val : 0); }
ModInt operator+(const ModInt &x) const { return ModInt(*this) += x; }
ModInt operator-(const ModInt &x) const { return ModInt(*this) -= x; }
ModInt operator*(const ModInt &x) const { return ModInt(*this) *= x; }
ModInt operator/(const ModInt &x) const { return ModInt(*this) /= x; }
friend ostream &operator<<(ostream &os, const ModInt &x) { return os << x.val; }
friend istream &operator>>(istream &is, ModInt &x) { ll val; is >> val; x = ModInt(val); return is; }
};
ModInt abs(const ModInt &x) { return x; }
struct Combinatorics {
int val; // "val!" and "mod" must be disjoint.
vector<ModInt> fact, fact_inv, inv;
Combinatorics(int val = 10000000) : val(val), fact(val + 1), fact_inv(val + 1), inv(val + 1) {
fact[0] = 1;
FOR(i, 1, val + 1) fact[i] = fact[i - 1] * i;
fact_inv[val] = ModInt(1) / fact[val];
for (int i = val; i > 0; --i) fact_inv[i - 1] = fact_inv[i] * i;
FOR(i, 1, val + 1) inv[i] = fact[i - 1] * fact_inv[i];
}
ModInt nCk(int n, int k) {
if (n < 0 || n < k || k < 0) return ModInt(0);
// assert(n <= val && k <= val);
return fact[n] * fact_inv[k] * fact_inv[n - k];
}
ModInt nPk(int n, int k) {
if (n < 0 || n < k || k < 0) return ModInt(0);
// assert(n <= val);
return fact[n] * fact_inv[n - k];
}
ModInt nHk(int n, int k) {
if (n < 0 || k < 0) return ModInt(0);
return (k == 0 ? ModInt(1) : nCk(n + k - 1, k));
}
};
template <typename T>
function<vector<T>(const vector<T>&, const vector<T>&)> mul = [](const vector<T> &a, const vector<T> &b) {
int n = a.size(), m = b.size();
vector<T> res(n + m - 1, T(0));
REP(i, n) REP(j, m) res[i + j] += a[i] * b[j];
return res;
};
template <typename T>
function<bool(const T&, T&)> sqr = [](const T &a, T &res) {
res = T(sqrt(a));
return true;
};
template <typename T>
function<vector<T>(const vector<T>&, const vector<T>&)> mul = [](const vector<T> &a, const vector<T> &b) {
int n = a.size(), m = b.size();
vector<T> res(n + m - 1, T(0));
REP(i, n) REP(j, m) res[i + j] += a[i] * b[j];
return res;
};
template <typename T>
function<bool(const T&, T&)> sqr = [](const T &a, T &res) {
return false;
};
template <typename T>
struct FPS {
vector<T> co;
FPS(int deg = 0) : co(deg + 1, T(0)) {}
FPS(const vector<T> &co) : co(co) {}
FPS(initializer_list<T> init) : co(init.begin(), init.end()) {}
template <typename InputIter> FPS(InputIter first, InputIter last) : co(first, last) {}
inline const T &operator[](int term) const { return co[term]; }
inline T &operator[](int term) { return co[term]; }
void resize(int deg) {
int prev = co.size();
co.resize(deg + 1);
if (prev < deg + 1) fill(co.begin() + prev, co.end(), T(0));
}
void shrink() { while (co.size() > 1 && co.back() == T(0)) co.pop_back(); }
int degree() const { return static_cast<int>(co.size()) - 1; }
FPS &operator=(const vector<T> &new_co) {
co.resize(new_co.size());
copy(ALL(new_co), co.begin());
return *this;
}
FPS &operator=(const FPS &x) {
co.resize(x.co.size());
copy(ALL(x.co), co.begin());
return *this;
}
FPS &operator+=(const FPS &x) {
int n = x.co.size();
if (n > co.size()) resize(n - 1);
REP(i, n) co[i] += x.co[i];
return *this;
}
FPS &operator-=(const FPS &x) {
int n = x.co.size();
if (n > co.size()) resize(n - 1);
REP(i, n) co[i] -= x.co[i];
return *this;
}
FPS &operator*=(T x) {
for (T &e : co) e *= x;
return *this;
}
FPS &operator*=(const FPS &x) { return *this = mul<T>(co, x.co); }
FPS &operator/=(T x) {
assert(x != T(0));
T inv_x = T(1) / x;
for (T &e : co) e *= inv_x;
return *this;
}
FPS &operator/=(const FPS &x) {
if (x.co.size() > co.size()) return *this = FPS();
int n = co.size() - x.co.size() + 1;
FPS a(co.rbegin(), co.rbegin() + n), b(x.co.rbegin(), x.co.rbegin() + min(static_cast<int>(x.co.size()), n));
b = b.inv(n - 1);
a *= b;
return *this = FPS(a.co.rend() - n, a.co.rend());
}
FPS &operator%=(const FPS &x) {
*this -= *this / x * x;
co.resize(static_cast<int>(x.co.size()) - 1);
if (co.empty()) co = {T(0)};
return *this;
}
FPS &operator<<=(int n) {
co.insert(co.begin(), n, T(0));
return *this;
}
FPS &operator>>=(int n) {
if (co.size() < n) return *this = FPS();
co.erase(co.begin(), co.begin() + n);
return *this;
}
bool operator==(const FPS &x) const {
FPS a(*this), b(x);
a.shrink(); b.shrink();
int n = a.co.size();
if (n != b.co.size()) return false;
REP(i, n) if (a.co[i] != b.co[i]) return false;
return true;
}
bool operator!=(const FPS &x) const { return !(*this == x); }
FPS operator+() const { return *this; }
FPS operator-() const {
FPS res(*this);
for (T &e : res.co) e = T(-e);
return res;
}
FPS operator+(const FPS &x) const { return FPS(*this) += x; }
FPS operator-(const FPS &x) const { return FPS(*this) -= x; }
FPS operator*(T x) const { return FPS(*this) *= x; }
FPS operator*(const FPS &x) const { return FPS(*this) *= x; }
FPS operator/(T x) const { return FPS(*this) /= x; }
FPS operator/(const FPS &x) const { return FPS(*this) /= x; }
FPS operator%(const FPS &x) const { return FPS(*this) %= x; }
FPS operator<<(int n) const { return FPS(*this) <<= n; }
FPS operator>>(int n) const { return FPS(*this) >>= n; }
T horner(T val) const {
T res = T(0);
for (int i = static_cast<int>(co.size()) - 1; i >= 0; --i) (res *= val) += co[i];
return res;
}
FPS differential() const {
int n = co.size();
assert(n >= 1);
FPS res(n - 1);
FOR(i, 1, n) res.co[i - 1] = co[i] * T(i);
return res;
}
FPS integral() const {
int n = co.size();
FPS res(n + 1);
REP(i, n) res[i + 1] = co[i] / T(i + 1);
return res;
}
FPS exp(int deg = -1) const {
assert(co[0] == T(0));
if (deg == -1) deg = static_cast<int>(co.size()) - 1;
FPS one({T(1)}), res = one;
for (int i = 1; i <= deg; i <<= 1) {
res *= FPS(co.begin(), co.begin() + min(static_cast<int>(co.size()), i << 1)) - res.log((i << 1) - 1) + one;
res.co.resize(i << 1);
}
res.co.resize(deg + 1);
return res;
}
FPS inv(int deg = -1) const {
assert(co[0] != T(0));
if (deg == -1) deg = static_cast<int>(co.size()) - 1;
FPS res({T(1) / co[0]});
for (int i = 1; i <= deg; i <<= 1) {
res = res + res - res * res * FPS(co.begin(), co.begin() + min(static_cast<int>(co.size()), i << 1));
res.co.resize(i << 1);
}
res.co.resize(deg + 1);
return res;
}
FPS log(int deg = -1) const {
assert(co[0] == T(1));
if (deg == -1) deg = static_cast<int>(co.size()) - 1;
FPS integrand = differential() * inv(deg - 1);
integrand.co.resize(deg);
return integrand.integral();
}
FPS pow(ll exponent, int deg = -1) const {
int n = co.size();
if (deg == -1) deg = n - 1;
REP(i, n) {
if (co[i] != T(0)) {
ll shift = exponent * i;
if (shift > deg) break;
T tmp = 1, base = co[i];
ll e = exponent;
while (e > 0) {
if (e & 1) tmp *= base;
base *= base;
e >>= 1;
}
return ((((*this >> i) * (T(1) / co[i])).log(deg - shift) * T(exponent)).exp(deg - shift) * tmp) << shift;
}
}
return FPS(deg);
}
FPS mod_pow(ll exponent, const FPS &md) const {
FPS inv_rev_md = FPS(md.co.rbegin(), md.co.rend()).inv();
int deg_of_md = md.co.size();
function<void(FPS&, const FPS&)> mod_mul = [&](FPS &multiplicand, const FPS &multiplier) {
multiplicand *= multiplier;
if (deg_of_md <= multiplicand.co.size()) {
int n = multiplicand.co.size() - deg_of_md + 1;
FPS quotient = FPS(multiplicand.co.rbegin(), multiplicand.co.rbegin() + n) * FPS(inv_rev_md.co.begin(), inv_rev_md.co.begin() + min(static_cast<int>(inv_rev_md.co.size()), n));
multiplicand -= FPS(quotient.co.rend() - n, quotient.co.rend()) * md;
}
multiplicand.co.resize(deg_of_md - 1);
if (multiplicand.co.empty()) multiplicand.co = {T(0)};
};
FPS res({T(1)}), base = *this;
mod_mul(base, res);
while (exponent > 0) {
if (exponent & 1) mod_mul(res, base);
mod_mul(base, base);
exponent >>= 1;
}
return res;
}
FPS sqrt(int deg = -1) const {
int n = co.size();
if (deg == -1) deg = n - 1;
if (co[0] == T(0)) {
FOR(i, 1, n) {
if (co[i] == T(0)) continue;
if (i & 1) return FPS(-1);
int shift = i >> 1;
if (deg < shift) break;
FPS res = (*this >> i).sqrt(deg - shift);
if (res.co.empty()) return FPS(-1);
res <<= shift;
res.resize(deg);
return res;
}
return FPS(deg);
}
T s;
if (!sqr<T>(co[0], s)) return FPS(-1);
FPS res({s});
T half = T(1) / T(2);
for (int i = 1; i <= deg; i <<= 1) {
(res += FPS(co.begin(), co.begin() + min(static_cast<int>(co.size()), i << 1)) * res.inv((i << 1) - 1)) *= half;
}
res.resize(deg);
return res;
}
FPS translate(T c) const {
int n = co.size();
vector<T> fact(n, T(1)), inv_fact(n, T(1));
FOR(i, 1, n) fact[i] = fact[i - 1] * T(i);
inv_fact[n - 1] = T(1) / fact[n - 1];
for (int i = n - 1; i > 0; --i) inv_fact[i - 1] = inv_fact[i] * T(i);
vector<T> g(n), ex(n);
REP(i, n) g[n - 1 - i] = co[i] * fact[i];
T pow_c = T(1);
REP(i, n) {
ex[i] = pow_c * inv_fact[i];
pow_c *= c;
}
vector<T> conv = mul<T>(g, ex);
FPS res(n - 1);
REP(i, n) res[i] = conv[n - 1 - i] * inv_fact[i];
return res;
}
};
namespace FFT {
using Real = long double;
struct Complex {
Real re, im;
Complex(Real re = 0, Real im = 0) : re(re), im(im) {}
inline Complex operator+(const Complex &x) const { return Complex(re + x.re, im + x.im); }
inline Complex operator-(const Complex &x) const { return Complex(re - x.re, im - x.im); }
inline Complex operator*(const Complex &x) const { return Complex(re * x.re - im * x.im, re * x.im + im * x.re); }
inline Complex mul_real(Real r) const { return Complex(re * r, im * r); }
inline Complex mul_pin(Real r) const { return Complex(-im * r, re * r); }
inline Complex conj() const { return Complex(re, -im); }
};
vector<int> butterfly{0};
vector<vector<Complex> > zeta{{{1, 0}}};
void calc(int n) {
int prev_n = butterfly.size();
if (n <= prev_n) return;
butterfly.resize(n);
int prev_lg = zeta.size(), lg = __builtin_ctz(n);
FOR(i, 1, prev_n) butterfly[i] <<= lg - prev_lg;
FOR(i, prev_n, n) butterfly[i] = (butterfly[i >> 1] >> 1) | ((i & 1) << (lg - 1));
zeta.resize(lg);
FOR(i, prev_lg, lg) {
zeta[i].resize(1 << i);
Real angle = -M_PI * 2 / (1 << (i + 1));
REP(j, 1 << (i - 1)) {
zeta[i][j << 1] = zeta[i - 1][j];
Real theta = angle * ((j << 1) + 1);
zeta[i][(j << 1) + 1] = {cos(theta), sin(theta)};
}
}
}
void sub_dft(vector<Complex> &a) {
int n = a.size();
// assert(__builtin_popcount(n) == 1);
calc(n);
int shift = __builtin_ctz(butterfly.size()) - __builtin_ctz(n);
REP(i, n) {
int j = butterfly[i] >> shift;
if (i < j) swap(a[i], a[j]);
}
for (int block = 1; block < n; block <<= 1) {
int den = __builtin_ctz(block);
for (int i = 0; i < n; i += (block << 1)) REP(j, block) {
Complex tmp = a[i + j + block] * zeta[den][j];
a[i + j + block] = a[i + j] - tmp;
a[i + j] = a[i + j] + tmp;
}
}
}
template <typename T>
vector<Complex> dft(const vector<T> &a) {
int sz = a.size(), lg = 1;
while ((1 << lg) < sz) ++lg;
vector<Complex> c(1 << lg);
REP(i, sz) c[i].re = a[i];
sub_dft(c);
return c;
}
vector<Real> real_idft(vector<Complex> &a) {
int n = a.size(), half = n >> 1, quarter = half >> 1;
// assert(__builtin_popcount(n) == 1);
calc(n);
a[0] = (a[0] + a[half] + (a[0] - a[half]).mul_pin(1)).mul_real(0.5);
int den = __builtin_ctz(half);
FOR(i, 1, quarter) {
int j = half - i;
Complex tmp1 = a[i] + a[j].conj(), tmp2 = ((a[i] - a[j].conj()) * zeta[den][j]).mul_pin(1);
a[i] = (tmp1 - tmp2).mul_real(0.5);
a[j] = (tmp1 + tmp2).mul_real(0.5).conj();
}
if (quarter > 0) a[quarter] = a[quarter].conj();
a.resize(half);
sub_dft(a);
reverse(a.begin() + 1, a.end());
Real r = 1.0 / half;
vector<Real> res(n);
REP(i, n) res[i] = (i & 1 ? a[i >> 1].im : a[i >> 1].re) * r;
return res;
}
void idft(vector<Complex> &a) {
int n = a.size();
sub_dft(a);
reverse(a.begin() + 1, a.end());
Real r = 1.0 / n;
REP(i, n) a[i] = a[i].mul_real(r);
}
template <typename T>
vector<Real> convolution(const vector<T> &a, const vector<T> &b) {
int a_sz = a.size(), b_sz = b.size(), sz = a_sz + b_sz - 1, lg = 1;
while ((1 << lg) < sz) ++lg;
int n = 1 << lg;
vector<Complex> c(n);
REP(i, a_sz) c[i].re = a[i];
REP(i, b_sz) c[i].im = b[i];
sub_dft(c);
int half = n >> 1;
c[0] = Complex(c[0].re * c[0].im, 0);
FOR(i, 1, half) {
Complex i_square = c[i] * c[i], j_square = c[n - i] * c[n - i];
c[i] = (j_square.conj() - i_square).mul_pin(0.25);
c[n - i] = (i_square.conj() - j_square).mul_pin(0.25);
}
c[half] = Complex(c[half].re * c[half].im, 0);
vector<Real> res = real_idft(c);
res.resize(sz);
return res;
}
};
vector<ModInt> mod_convolution(const vector<ModInt> &a, const vector<ModInt> &b, const int pre = 15) {
using Complex = FFT::Complex;
int a_sz = a.size(), b_sz = b.size(), sz = a_sz + b_sz - 1, lg = 1;
while ((1 << lg) < sz) ++lg;
int n = 1 << lg;
vector<Complex> A(n), B(n);
REP(i, a_sz) {
int ai = a[i].val;
A[i] = Complex(ai & ((1 << pre) - 1), ai >> pre);
}
REP(i, b_sz) {
int bi = b[i].val;
B[i] = Complex(bi & ((1 << pre) - 1), bi >> pre);
}
FFT::sub_dft(A);
FFT::sub_dft(B);
int half = n >> 1;
Complex tmp_a = A[0], tmp_b = B[0];
A[0] = {tmp_a.re * tmp_b.re, tmp_a.im * tmp_b.im};
B[0] = {tmp_a.re * tmp_b.im + tmp_a.im * tmp_b.re, 0};
FOR(i, 1, half) {
int j = n - i;
Complex a_l_i = (A[i] + A[j].conj()).mul_real(0.5), a_h_i = (A[j].conj() - A[i]).mul_pin(0.5);
Complex b_l_i = (B[i] + B[j].conj()).mul_real(0.5), b_h_i = (B[j].conj() - B[i]).mul_pin(0.5);
Complex a_l_j = (A[j] + A[i].conj()).mul_real(0.5), a_h_j = (A[i].conj() - A[j]).mul_pin(0.5);
Complex b_l_j = (B[j] + B[i].conj()).mul_real(0.5), b_h_j = (B[i].conj() - B[j]).mul_pin(0.5);
A[i] = a_l_i * b_l_i + (a_h_i * b_h_i).mul_pin(1);
B[i] = a_l_i * b_h_i + a_h_i * b_l_i;
A[j] = a_l_j * b_l_j + (a_h_j * b_h_j).mul_pin(1);
B[j] = a_l_j * b_h_j + a_h_j * b_l_j;
}
tmp_a = A[half]; tmp_b = B[half];
A[half] = {tmp_a.re * tmp_b.re, tmp_a.im * tmp_b.im};
B[half] = {tmp_a.re * tmp_b.im + tmp_a.im * tmp_b.re, 0};
FFT::idft(A);
FFT::idft(B);
vector<ModInt> res(sz);
ModInt tmp1 = 1 << pre, tmp2 = 1LL << (pre << 1);
REP(i, sz) {
res[i] += static_cast<ll>(A[i].re + 0.5);
res[i] += tmp1 * static_cast<ll>(B[i].re + 0.5);
res[i] += tmp2 * static_cast<ll>(A[i].im + 0.5);
}
return res;
}
int main() {
mul<ModInt> = [&](const vector<ModInt> &a, const vector<ModInt> &b) {
return mod_convolution(a, b);
};
int k, n; cin >> k >> n;
FPS<ModInt> fps(k);
while (n--) {
int x; cin >> x;
if (x <= k) fps[x] = 1;
}
fps = -fps;
fps[0] += 1;
cout << fps.inv(k)[k] << '\n';
return 0;
}