結果

問題 No.1035 Color Box
ユーザー tanimani364
提出日時 2020-04-24 22:48:46
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 24 ms / 2,000 ms
コード長 16,014 bytes
コンパイル時間 2,654 ms
コンパイル使用メモリ 207,460 KB
最終ジャッジ日時 2025-01-10 00:18:54
ジャッジサーバーID
(参考情報)
judge5 / judge5
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ファイルパターン 結果
sample AC * 2
other AC * 36
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ソースコード

diff #
プレゼンテーションモードにする

#include<bits/stdc++.h>
#define rep(i,a) for(int i=(int)0;i<(int)a;++i)
#define rrep(i,a) for(int i=(int)a-1;i>=0;--i)
#define REP(i,a,b) for(int i=(int)a;i<(int)b;++i)
#define RREP(i,a,b) for(int i=(int)a-1;i>=b;--i)
#define pb push_back
#define eb emplace_back
#define all(x) x.begin(),x.end()
#define rall(x) x.rbegin(),x.rend()
typedef std::vector<int> vi;
typedef std::vector<std::vector<int>> vvi;
typedef std::vector<long long> vl;
typedef std::vector<std::vector<long long>> vvl;
#define out(x) cout<<x<<"\n";
using ll=long long;
constexpr ll mod = 1e9 + 7;
constexpr ll INF = 1LL << 60;
template<class T> inline bool chmin(T& a, T b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template<class T> inline bool chmax(T& a, T b) {
if (a < b) {
a = b;
return true;
}
return false;
}
ll gcd(ll n, ll m) {
ll tmp;
while (m!=0) {
tmp = n % m;
n = m;
m = tmp;
}
return n;
}
ll lcm(ll n, ll m) {
return abs(n) / gcd(n, m)*abs(m);//gl=xy
}
using namespace std;
#define int64_t ll
template< int mod >
struct ModInt {
int x;
ModInt() : x(0) {}
ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
ModInt &operator+=(const ModInt &p) {
if((x += p.x) >= mod) x -= mod;
return *this;
}
ModInt &operator-=(const ModInt &p) {
if((x += mod - p.x) >= mod) x -= mod;
return *this;
}
ModInt &operator*=(const ModInt &p) {
x = (int) (1LL * x * p.x % mod);
return *this;
}
ModInt &operator/=(const ModInt &p) {
*this *= p.inverse();
return *this;
}
ModInt operator-() const { return ModInt(-x); }
ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
bool operator==(const ModInt &p) const { return x == p.x; }
bool operator!=(const ModInt &p) const { return x != p.x; }
ModInt inverse() const {
int a = x, b = mod, u = 1, v = 0, t;
while(b > 0) {
t = a / b;
swap(a -= t * b, b);
swap(u -= t * v, v);
}
return ModInt(u);
}
ModInt pow(int64_t n) const {
ModInt ret(1), mul(x);
while(n > 0) {
if(n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
friend ostream &operator<<(ostream &os, const ModInt &p) {
return os << p.x;
}
friend istream &operator>>(istream &is, ModInt &a) {
int64_t t;
is >> t;
a = ModInt< mod >(t);
return (is);
}
static int get_mod() { return mod; }
};
using modint = ModInt< mod >;
template< typename T >
struct Combination {
vector< T > _fact, _rfact, _inv;
Combination(int sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {
_fact[0] = _rfact[sz] = _inv[0] = 1;
for(int i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i;
_rfact[sz] /= _fact[sz];
for(int i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1);
for(int i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1];
}
inline T fact(int k) const { return _fact[k]; }
inline T rfact(int k) const { return _rfact[k]; }
inline T inv(int k) const { return _inv[k]; }
T P(int n, int r) const {
if(r < 0 || n < r) return 0;
return fact(n) * rfact(n - r);
}
T C(int p, int q) const {
if(q < 0 || p < q) return 0;
return fact(p) * rfact(q) * rfact(p - q);
}
T H(int n, int r) const {
if(n < 0 || r < 0) return (0);
return r == 0 ? 1 : C(n + r - 1, r);
}
};
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;
}
};
template< typename T >
struct ArbitraryModConvolution {
using real = FastFourierTransform::real;
using C = FastFourierTransform::C;
ArbitraryModConvolution() = default;
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;
}
};
template< typename T >
struct FormalPowerSeries : vector< T > {
using vector< T >::vector;
using P = FormalPowerSeries;
using MULT = function< P(P, P) >;
static MULT &get_mult() {
static MULT mult = nullptr;
return mult;
}
static void set_fft(MULT f) {
get_mult() = f;
}
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 T &r) {
if(this->empty()) this->resize(1);
(*this)[0] += r;
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];
shrink();
return *this;
}
P &operator-=(const T &r) {
if(this->empty()) this->resize(1);
(*this)[0] -= r;
shrink();
return *this;
}
P &operator*=(const T &v) {
const int n = (int) this->size();
for(int k = 0; k < n; k++) (*this)[k] *= v;
return *this;
}
P &operator*=(const P &r) {
if(this->empty() || r.empty()) {
this->clear();
return *this;
}
assert(get_mult() != nullptr);
return *this = get_mult()(*this, r);
}
P &operator%=(const P &r) {
return *this -= *this / r * 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 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 pre(int sz) const {
return P(begin(*this), begin(*this) + min((int) this->size(), sz));
}
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;
}
P rev(int deg = -1) const {
P ret(*this);
if(deg != -1) ret.resize(deg, T(0));
reverse(begin(ret), end(ret));
return ret;
}
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;
}
// 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);
}
// F(0) must be 1
P log(int deg = -1) const {
assert((*this)[0] == 1);
const int n = (int) this->size();
if(deg == -1) deg = n;
return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
}
P sqrt(int deg = -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) << (i / 2);
if(ret.size() < deg) ret.resize(deg, T(0));
return ret;
}
}
return P(deg, 0);
}
P ret({T(1)});
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);
}
// F(0) must be 0
P exp(int deg = -1) const {
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);
}
P pow(int64_t k, int deg = -1) const {
const int n = (int) this->size();
if(deg == -1) deg = n;
for(int i = 0; i < n; i++) {
if((*this)[i] != T(0)) {
T rev = T(1) / (*this)[i];
P C(*this * rev);
P D(n - i);
for(int j = i; j < n; j++) D[j - i] = C[j];
D = (D.log() * k).exp() * (*this)[i].pow(k);
P E(deg);
if(i * k > deg) return E;
auto S = i * k;
for(int j = 0; j + S < deg && j < D.size(); j++) E[j + S] = D[j];
return E;
}
}
return *this;
}
T eval(T x) const {
T r = 0, w = 1;
for(auto &v : *this) {
r += w * v;
w *= x;
}
return r;
}
};
template< typename T >
T factorial(int64_t n) {
if(n >= T::get_mod()) return 0;
if(n == 0) return 1;
const int64_t sn = sqrt(n);
const T sn_inv = T(1) / sn;
Combination< modint > comb(sn);
using P = vector< T >;
ArbitraryModConvolution< T > fft;
using FPS = FormalPowerSeries< T >;
auto mult = [&](const typename FPS::P &a, const typename FPS::P &b) {
auto ret = fft.multiply(a, b);
return typename FPS::P(ret.begin(), ret.end());
};
FPS::set_fft(mult);
auto shift = [&](const P &f, T dx) {
int n = (int) f.size();
T a = dx * sn_inv;
auto p1 = P(f);
for(int i = 0; i < n; i++) {
T d = comb.rfact(i) * comb.rfact((n - 1) - i);
if(((n - 1 - i) & 1)) d = -d;
p1[i] *= d;
}
auto p2 = P(2 * n);
for(int i = 0; i < p2.size(); i++) {
p2[i] = (a.x + i - n) <= 0 ? 1 : a + i - n;
}
for(int i = 1; i < p2.size(); i++) {
p2[i] *= p2[i - 1];
}
T prod = p2[2 * n - 1];
T prod_inv = T(1) / prod;
for(int i = 2 * n - 1; i > 0; --i) {
p2[i] = prod_inv * p2[i - 1];
prod_inv *= a + i - n;
}
p2[0] = prod_inv;
auto p3 = fft.multiply(p1, p2, (int) p2.size());
p1 = P(p3.begin() + p1.size(), p3.begin() + p2.size());
prod = 1;
for(int i = 0; i < n; i++) {
prod *= a + n - 1 - i;
}
for(int i = n - 1; i >= 0; --i) {
p1[i] *= prod;
prod *= p2[n + i] * (a + i - n);
}
return p1;
};
function< P(int) > rec = [&](int64_t n) {
if(n == 1) return P({1, 1 + sn});
int64_t nh = n >> 1;
auto a1 = rec(nh);
auto a2 = shift(a1, nh);
auto b1 = shift(a1, sn * nh);
auto b2 = shift(a1, sn * nh + nh);
for(int i = 0; i <= nh; i++) a1[i] *= a2[i];
for(int i = 1; i <= nh; i++) a1.emplace_back(b1[i] * b2[i]);
if(n & 1) {
for(int64_t i = 0; i < n; i++) {
a1[i] *= n + 1LL * sn * i;
}
T prod = 1;
for(int64_t i = 1LL * n * sn; i < 1LL * n * sn + n; i++) {
prod *= (i + 1);
}
a1.push_back(prod);
}
return a1;
};
auto vs = rec(sn);
T ret = 1;
for(int64_t i = 0; i < sn; i++) ret *= vs[i];
for(int64_t i = 1LL * sn * sn + 1; i <= n; i++) ret *= i;
return ret;
}
void solve()
{
ll n,m;
cin >> n >> m;
modint ans = 0;
Combination<modint> c(m + 5);
modint sum = 0;
rep(i,m){
modint x = -1;
modint y = m - i;
ans += x.pow(i) * c.C(m, i) * y.pow(n);
}
cout << ans << endl;
}
int main(){
ios::sync_with_stdio(false);
cin.tie(0);
cout<<fixed<<setprecision(15);
solve();
return 0;
}
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