結果
| 問題 | No.3046 yukicoderの過去問 |
| ユーザー |
 ei1333333
|
| 提出日時 | 2024-04-24 01:45:08 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 17,350 bytes |
| コンパイル時間 | 2,760 ms |
| コンパイル使用メモリ | 224,608 KB |
| 実行使用メモリ | 20,612 KB |
| 最終ジャッジ日時 | 2024-11-06 08:24:18 |
| 合計ジャッジ時間 | 4,253 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | WA | - |
| testcase_01 | WA | - |
| testcase_02 | AC | 2 ms
6,816 KB |
| testcase_03 | WA | - |
| testcase_04 | WA | - |
| testcase_05 | WA | - |
| testcase_06 | WA | - |
| testcase_07 | WA | - |
| testcase_08 | WA | - |
ソースコード
#line 1 "test/verify/yukicoder-3046.test.cpp"
// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/3046
#line 1 "template/template.hpp"
#include<bits/stdc++.h>
using namespace std;
using int64 = long long;
const int mod = 1e9 + 7;
const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;
struct IoSetup {
IoSetup() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(10);
cerr << fixed << setprecision(10);
}
} iosetup;
template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 >& p) {
os << p.first << " " << p.second;
return os;
}
template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
is >> p.first >> p.second;
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 != v.size() ? " " : "");
}
return os;
}
template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
for(T &in : v) is >> in;
return is;
}
template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }
template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }
template< typename T = int64 >
vector< T > make_v(size_t a) {
return vector< T >(a);
}
template< typename T, typename... Ts >
auto make_v(size_t a, Ts... ts) {
return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...));
}
template< typename T, typename V >
typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) {
t = v;
}
template< typename T, typename V >
typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) {
for(auto &e : t) fill_v(e, v);
}
template< typename F >
struct FixPoint : F {
explicit FixPoint(F &&f) : F(forward< F >(f)) {}
template< typename... Args >
decltype(auto) operator()(Args &&... args) const {
return F::operator()(*this, forward< Args >(args)...);
}
};
template< typename F >
inline decltype(auto) MFP(F &&f) {
return FixPoint< F >{forward< F >(f)};
}
#line 4 "test/verify/yukicoder-3046.test.cpp"
template< uint32_t mod_, bool fast = false >
struct MontgomeryModInt {
using mint = MontgomeryModInt;
using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 ret = mod_;
for (i32 i = 0; i < 4; i++) ret *= 2 - mod_ * ret;
return ret;
}
static constexpr u32 r = get_r();
static constexpr u32 n2 = -u64(mod_) % mod_;
static_assert(r * mod_ == 1, "invalid, r * mod != 1");
static_assert(mod_ < (1 << 30), "invalid, mod >= 2 ^ 30");
static_assert((mod_ & 1) == 1, "invalid, mod % 2 == 0");
u32 x;
MontgomeryModInt(): x{} {}
MontgomeryModInt(const i64 &a)
: x(reduce(u64(fast ? a : (a % mod() + mod())) * n2)) {}
static constexpr u32 reduce(const u64 &b) {
return u32(b >> 32) + mod() - u32((u64(u32(b) * r) * mod()) >> 32);
}
mint &operator+=(const mint &p) {
if (i32(x += p.x - 2 * mod()) < 0) x += 2 * mod();
return *this;
}
mint &operator-=(const mint &p) {
if (i32(x -= p.x) < 0) x += 2 * mod();
return *this;
}
mint &operator*=(const mint &p) {
x = reduce(u64(x) * p.x);
return *this;
}
mint &operator/=(const mint &p) {
*this *= p.inv();
return *this;
}
mint operator-() const { return mint() - *this; }
mint operator+(const mint &p) const { return mint(*this) += p; }
mint operator-(const mint &p) const { return mint(*this) -= p; }
mint operator*(const mint &p) const { return mint(*this) *= p; }
mint operator/(const mint &p) const { return mint(*this) /= p; }
bool operator==(const mint &p) const {
return (x >= mod() ? x - mod() : x) == (p.x >= mod() ? p.x - mod() : p.x);
}
bool operator!=(const mint &p) const {
return (x >= mod() ? x - mod() : x) != (p.x >= mod() ? p.x - mod() : p.x);
}
u32 val() const {
u32 ret = reduce(x);
return ret >= mod() ? ret - mod() : ret;
}
mint pow(u64 n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
mint inv() const {
return pow(mod() - 2);
}
friend ostream &operator<<(ostream &os, const mint &p) {
return os << p.val();
}
friend istream &operator>>(istream &is, mint &a) {
i64 t;
is >> t;
a = mint(t);
return is;
}
static constexpr u32 mod() { return mod_; }
};
template< uint32_t mod >
using modint = MontgomeryModInt< mod >;
using modint998244353 = modint< 998244353 >;
using modint1000000007 = modint< 1000000007 >;
#line 2 "math/fps/formal-power-series.hpp"
#line 1 "math/fft/fast-fourier-transform.hpp"
namespace FastFourierTransform {
using real = double;
struct C {
real x, y;
C() : x(0), y(0) {}
C(real x, real y) : x(x), y(y) {}
inline C operator+(const C &c) const { return C(x + c.x, y + c.y); }
inline C operator-(const C &c) const { return C(x - c.x, y - c.y); }
inline C operator*(const C &c) const { return C(x * c.x - y * c.y, x * c.y + y * c.x); }
inline C conj() const { return C(x, -y); }
};
const real PI = acosl(-1);
int base = 1;
vector< C > rts = { {0, 0},
{1, 0} };
vector< int > rev = {0, 1};
void ensure_base(int nbase) {
if(nbase <= base) return;
rev.resize(1 << nbase);
rts.resize(1 << nbase);
for(int i = 0; i < (1 << nbase); i++) {
rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
}
while(base < nbase) {
real angle = PI * 2.0 / (1 << (base + 1));
for(int i = 1 << (base - 1); i < (1 << base); i++) {
rts[i << 1] = rts[i];
real angle_i = angle * (2 * i + 1 - (1 << base));
rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i));
}
++base;
}
}
void fft(vector< C > &a, int n) {
assert((n & (n - 1)) == 0);
int zeros = __builtin_ctz(n);
ensure_base(zeros);
int shift = base - zeros;
for(int i = 0; i < n; i++) {
if(i < (rev[i] >> shift)) {
swap(a[i], a[rev[i] >> shift]);
}
}
for(int k = 1; k < n; k <<= 1) {
for(int i = 0; i < n; i += 2 * k) {
for(int j = 0; j < k; j++) {
C z = a[i + j + k] * rts[j + k];
a[i + j + k] = a[i + j] - z;
a[i + j] = a[i + j] + z;
}
}
}
}
vector< int64_t > multiply(const vector< int > &a, const vector< int > &b) {
int need = (int) a.size() + (int) b.size() - 1;
int nbase = 1;
while((1 << nbase) < need) nbase++;
ensure_base(nbase);
int sz = 1 << nbase;
vector< C > fa(sz);
for(int i = 0; i < sz; i++) {
int x = (i < (int) a.size() ? a[i] : 0);
int y = (i < (int) b.size() ? b[i] : 0);
fa[i] = C(x, y);
}
fft(fa, sz);
C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);
for(int i = 0; i <= (sz >> 1); i++) {
int j = (sz - i) & (sz - 1);
C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;
fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;
fa[i] = z;
}
for(int i = 0; i < (sz >> 1); i++) {
C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;
C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * rts[(sz >> 1) + i];
fa[i] = A0 + A1 * s;
}
fft(fa, sz >> 1);
vector< int64_t > ret(need);
for(int i = 0; i < need; i++) {
ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x);
}
return ret;
}
};
#line 2 "math/fft/arbitrary-mod-convolution.hpp"
/*
* @brief Arbitrary Mod Convolution(任意mod畳み込み)
*/
template< typename T >
struct ArbitraryModConvolution {
using real = FastFourierTransform::real;
using C = FastFourierTransform::C;
ArbitraryModConvolution() = default;
static vector< T > multiply(const vector< T > &a, const vector< T > &b, int need = -1) {
if(need == -1) need = a.size() + b.size() - 1;
int nbase = 0;
while((1 << nbase) < need) nbase++;
FastFourierTransform::ensure_base(nbase);
int sz = 1 << nbase;
vector< C > fa(sz);
for(int i = 0; i < a.size(); i++) {
fa[i] = C(a[i].x & ((1 << 15) - 1), a[i].x >> 15);
}
fft(fa, sz);
vector< C > fb(sz);
if(a == b) {
fb = fa;
} else {
for(int i = 0; i < b.size(); i++) {
fb[i] = C(b[i].x & ((1 << 15) - 1), b[i].x >> 15);
}
fft(fb, sz);
}
real ratio = 0.25 / sz;
C r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1);
for(int i = 0; i <= (sz >> 1); i++) {
int j = (sz - i) & (sz - 1);
C a1 = (fa[i] + fa[j].conj());
C a2 = (fa[i] - fa[j].conj()) * r2;
C b1 = (fb[i] + fb[j].conj()) * r3;
C b2 = (fb[i] - fb[j].conj()) * r4;
if(i != j) {
C c1 = (fa[j] + fa[i].conj());
C c2 = (fa[j] - fa[i].conj()) * r2;
C d1 = (fb[j] + fb[i].conj()) * r3;
C d2 = (fb[j] - fb[i].conj()) * r4;
fa[i] = c1 * d1 + c2 * d2 * r5;
fb[i] = c1 * d2 + c2 * d1;
}
fa[j] = a1 * b1 + a2 * b2 * r5;
fb[j] = a1 * b2 + a2 * b1;
}
fft(fa, sz);
fft(fb, sz);
vector< T > ret(need);
for(int i = 0; i < need; i++) {
int64_t aa = llround(fa[i].x);
int64_t bb = llround(fb[i].x);
int64_t cc = llround(fa[i].y);
aa = T(aa).x, bb = T(bb).x, cc = T(cc).x;
ret[i] = aa + (bb << 15) + (cc << 30);
}
return ret;
}
};
#line 4 "math/fps/formal-power-series.hpp"
/**
* @brief Formal Power Series(形式的冪級数)
*/
template< typename T >
struct FormalPowerSeries : vector< T > {
using vector< T >::vector;
using P = FormalPowerSeries;
using Conv = ArbitraryModConvolution< T >;
P pre(int deg) const {
return P(begin(*this), begin(*this) + min((int) this->size(), deg));
}
P rev(int deg = -1) const {
P ret(*this);
if(deg != -1) ret.resize(deg, T(0));
reverse(begin(ret), end(ret));
return ret;
}
void shrink() {
while(this->size() && this->back() == T(0)) this->pop_back();
}
P operator+(const P &r) const { return P(*this) += r; }
P operator+(const T &v) const { return P(*this) += v; }
P operator-(const P &r) const { return P(*this) -= r; }
P operator-(const T &v) const { return P(*this) -= v; }
P operator*(const P &r) const { return P(*this) *= r; }
P operator*(const T &v) const { return P(*this) *= v; }
P operator/(const P &r) const { return P(*this) /= r; }
P operator%(const P &r) const { return P(*this) %= r; }
P &operator+=(const P &r) {
if(r.size() > this->size()) this->resize(r.size());
for(int i = 0; i < r.size(); i++) (*this)[i] += r[i];
return *this;
}
P &operator-=(const P &r) {
if(r.size() > this->size()) this->resize(r.size());
for(int i = 0; i < r.size(); i++) (*this)[i] -= r[i];
return *this;
}
// https://judge.yosupo.jp/problem/convolution_mod
P &operator*=(const P &r) {
if(this->empty() || r.empty()) {
this->clear();
return *this;
}
auto ret = Conv::multiply(*this, r);
return *this = {begin(ret), end(ret)};
}
P &operator/=(const P &r) {
if(this->size() < r.size()) {
this->clear();
return *this;
}
int n = this->size() - r.size() + 1;
return *this = (rev().pre(n) * r.rev().inv(n)).pre(n).rev(n);
}
P &operator%=(const P &r) {
return *this -= *this / r * r;
}
// https://judge.yosupo.jp/problem/division_of_polynomials
pair< P, P > div_mod(const P &r) {
P q = *this / r;
return make_pair(q, *this - q * r);
}
P operator-() const {
P ret(this->size());
for(int i = 0; i < this->size(); i++) ret[i] = -(*this)[i];
return ret;
}
P &operator+=(const T &r) {
if(this->empty()) this->resize(1);
(*this)[0] += r;
return *this;
}
P &operator-=(const T &r) {
if(this->empty()) this->resize(1);
(*this)[0] -= r;
return *this;
}
P &operator*=(const T &v) {
for(int i = 0; i < this->size(); i++) (*this)[i] *= v;
return *this;
}
P dot(P r) const {
P ret(min(this->size(), r.size()));
for(int i = 0; i < ret.size(); i++) ret[i] = (*this)[i] * r[i];
return ret;
}
P operator>>(int sz) const {
if(this->size() <= sz) return {};
P ret(*this);
ret.erase(ret.begin(), ret.begin() + sz);
return ret;
}
P operator<<(int sz) const {
P ret(*this);
ret.insert(ret.begin(), sz, T(0));
return ret;
}
T operator()(T x) const {
T r = 0, w = 1;
for(auto &v : *this) {
r += w * v;
w *= x;
}
return r;
}
P diff() const {
const int n = (int) this->size();
P ret(max(0, n - 1));
for(int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i);
return ret;
}
P integral() const {
const int n = (int) this->size();
P ret(n + 1);
ret[0] = T(0);
for(int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / T(i + 1);
return ret;
}
// https://judge.yosupo.jp/problem/inv_of_formal_power_series
// F(0) must not be 0
P inv(int deg = -1) const {
assert(((*this)[0]) != T(0));
const int n = (int) this->size();
if(deg == -1) deg = n;
P ret({T(1) / (*this)[0]});
for(int i = 1; i < deg; i <<= 1) {
ret = (ret + ret - ret * ret * pre(i << 1)).pre(i << 1);
}
return ret.pre(deg);
}
// https://judge.yosupo.jp/problem/log_of_formal_power_series
// F(0) must be 1
P log(int deg = -1) const {
assert((*this)[0] == T(1));
const int n = (int) this->size();
if(deg == -1) deg = n;
return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
}
// https://judge.yosupo.jp/problem/sqrt_of_formal_power_series
P sqrt(int deg = -1, const function< T(T) > &get_sqrt = [](T) { return T(1); }) const {
const int n = (int) this->size();
if(deg == -1) deg = n;
if((*this)[0] == T(0)) {
for(int i = 1; i < n; i++) {
if((*this)[i] != T(0)) {
if(i & 1) return {};
if(deg - i / 2 <= 0) break;
auto ret = (*this >> i).sqrt(deg - i / 2, get_sqrt);
if(ret.empty()) return {};
ret = ret << (i / 2);
if(ret.size() < deg) ret.resize(deg, T(0));
return ret;
}
}
return P(deg, 0);
}
auto sqr = T(get_sqrt((*this)[0]));
if(sqr * sqr != (*this)[0]) return {};
P ret{sqr};
T inv2 = T(1) / T(2);
for(int i = 1; i < deg; i <<= 1) {
ret = (ret + pre(i << 1) * ret.inv(i << 1)) * inv2;
}
return ret.pre(deg);
}
P sqrt(const function< T(T) > &get_sqrt, int deg = -1) const {
return sqrt(deg, get_sqrt);
}
// https://judge.yosupo.jp/problem/exp_of_formal_power_series
// F(0) must be 0
P exp(int deg = -1) const {
if(deg == -1) deg = this->size();
assert((*this)[0] == T(0));
const int n = (int) this->size();
if(deg == -1) deg = n;
P ret({T(1)});
for(int i = 1; i < deg; i <<= 1) {
ret = (ret * (pre(i << 1) + T(1) - ret.log(i << 1))).pre(i << 1);
}
return ret.pre(deg);
}
// https://judge.yosupo.jp/problem/pow_of_formal_power_series
P pow(int64_t k, int deg = -1) const {
const int n = (int) this->size();
if(deg == -1) deg = n;
if(k == 0) {
P ret(deg, T(0));
ret[0] = T(1);
return ret;
}
for(int i = 0; i < n; i++) {
if(i * k > deg) return P(deg, T(0));
if((*this)[i] != T(0)) {
T rev = T(1) / (*this)[i];
P ret = (((*this * rev) >> i).log() * k).exp() * ((*this)[i].pow(k));
ret = (ret << (i * k)).pre(deg);
if(ret.size() < deg) ret.resize(deg, T(0));
return ret;
}
}
return *this;
}
// https://yukicoder.me/problems/no/215
P mod_pow(int64_t k, P g) const {
P modinv = g.rev().inv();
auto get_div = [&](P base) {
if(base.size() < g.size()) {
base.clear();
return base;
}
int n = base.size() - g.size() + 1;
return (base.rev().pre(n) * modinv.pre(n)).pre(n).rev(n);
};
P x(*this), ret{1};
while(k > 0) {
if(k & 1) {
ret *= x;
ret -= get_div(ret) * g;
ret.shrink();
}
x *= x;
x -= get_div(x) * g;
x.shrink();
k >>= 1;
}
return ret;
}
// https://judge.yosupo.jp/problem/polynomial_taylor_shift
P taylor_shift(T c) const {
int n = (int) this->size();
vector< T > fact(n), rfact(n);
fact[0] = rfact[0] = T(1);
for(int i = 1; i < n; i++) fact[i] = fact[i - 1] * T(i);
rfact[n - 1] = T(1) / fact[n - 1];
for(int i = n - 1; i > 1; i--) rfact[i - 1] = rfact[i] * T(i);
P p(*this);
for(int i = 0; i < n; i++) p[i] *= fact[i];
p = p.rev();
P bs(n, T(1));
for(int i = 1; i < n; i++) bs[i] = bs[i - 1] * c * rfact[i] * fact[i - 1];
p = (p * bs).pre(n);
p = p.rev();
for(int i = 0; i < n; i++) p[i] *= rfact[i];
return p;
}
};
template< typename Mint >
using FPS = FormalPowerSeries< Mint >;
template< typename Mint >
using FPS = FormalPowerSeries< Mint >;
#line 7 "test/verify/yukicoder-3046.test.cpp"
using mint = modint1000000007;
int main() {
int K, N;
cin >> K >> N;
FPS< mint > X(K + 1);
X[0] = 1;
for(int i = 0; i < N; i++) {
int x;
cin >> x;
if(x <= K) X[x] = -1;
}
cout << X.inv()[K] << endl;
}