結果

問題 No.1846 Good Binary Matrix
ユーザー satashunsatashun
提出日時 2023-05-18 07:03:17
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 330 ms / 2,000 ms
コード長 9,960 bytes
コンパイル時間 2,381 ms
コンパイル使用メモリ 205,380 KB
最終ジャッジ日時 2025-02-13 01:12:51
ジャッジサーバーID
(参考情報)
judge2 / judge1
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ファイルパターン 結果
other AC * 35
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ソースコード

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#pragma region satashun
// #pragma GCC optimize("Ofast")
// #pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
using pii = pair<int, int>;
template <class T>
using V = vector<T>;
template <class T>
using VV = V<V<T>>;
template <class T>
V<T> make_vec(size_t a) {
return V<T>(a);
}
template <class T, class... Ts>
auto make_vec(size_t a, Ts... ts) {
return V<decltype(make_vec<T>(ts...))>(a, make_vec<T>(ts...));
}
template <typename T, typename V>
void fill_vec(T& v, const V& val) {
v = val;
}
template <typename T, typename V>
void fill_vec(vector<T>& vec, const V& val) {
for (auto& v : vec) fill_vec(v, val);
}
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fi first
#define se second
#define rep(i, n) rep2(i, 0, n)
#define rep2(i, m, n) for (int i = m; i < (n); i++)
#define per(i, b) per2(i, 0, b)
#define per2(i, a, b) for (int i = int(b) - 1; i >= int(a); i--)
#define ALL(c) (c).begin(), (c).end()
#define SZ(x) ((int)(x).size())
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }
template <class T, class U>
void chmin(T& t, const U& u) {
if (t > u) t = u;
}
template <class T, class U>
void chmax(T& t, const U& u) {
if (t < u) t = u;
}
template <typename T>
int arglb(const V<T>& v, const T& x) {
return distance(v.begin(), lower_bound(ALL(v), x));
}
template <typename T>
int argub(const V<T>& v, const T& x) {
return distance(v.begin(), upper_bound(ALL(v), x));
}
template <class T>
void mkuni(vector<T>& v) {
sort(ALL(v));
v.erase(unique(ALL(v)), end(v));
}
template <class T>
vector<int> sort_by(const vector<T>& v, bool increasing = true) {
vector<int> res(v.size());
iota(res.begin(), res.end(), 0);
if (increasing) {
stable_sort(res.begin(), res.end(),
[&](int i, int j) { return v[i] < v[j]; });
} else {
stable_sort(res.begin(), res.end(),
[&](int i, int j) { return v[i] > v[j]; });
}
return res;
}
template <class T, class U>
istream& operator>>(istream& is, pair<T, U>& p) {
is >> p.first >> p.second;
return is;
}
template <class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
os << "(" << p.first << "," << p.second << ")";
return os;
}
template <class T>
istream& operator>>(istream& is, vector<T>& v) {
for (auto& x : v) {
is >> x;
}
return is;
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& v) {
os << "{";
rep(i, v.size()) {
if (i) os << ",";
os << v[i];
}
os << "}";
return os;
}
template <class T>
ostream& operator<<(ostream& os, const set<T>& ST) {
os << "{";
for (auto it = ST.begin(); it != ST.end(); ++it) {
if (it != ST.begin()) os << ",";
os << *it;
}
os << "}";
return os;
}
template <class T>
ostream& operator<<(ostream& os, const multiset<T>& ST) {
os << "{";
for (auto it = ST.begin(); it != ST.end(); ++it) {
if (it != ST.begin()) os << ",";
os << *it;
}
os << "}";
return os;
}
template <class T, class U>
ostream& operator<<(ostream& os, const map<T, U>& MP) {
for (auto it = MP.begin(); it != MP.end(); ++it) {
os << "(" << it->first << ": " << it->second << ")";
}
return os;
}
string to_string(__int128_t x) {
if (x == 0) return "0";
string result;
if (x < 0) {
result += "-";
x *= -1;
}
string t;
while (x) {
t.push_back('0' + x % 10);
x /= 10;
}
reverse(t.begin(), t.end());
return result + t;
}
ostream& operator<<(ostream& o, __int128_t x) { return o << to_string(x); }
#ifdef LOCAL
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
cerr << " " << H;
debug_out(T...);
}
#define debug(...) \
cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif
template <class T>
V<T>& operator+=(V<T>& vec, const T& v) {
for (auto& x : vec) x += v;
return vec;
}
template <class T>
V<T>& operator-=(V<T>& vec, const T& v) {
for (auto& x : vec) x -= v;
return vec;
}
// suc : 1 = newline, 2 = space
template <class T>
void print(T x, int suc = 1) {
cout << x;
if (suc == 1)
cout << "\n";
else if (suc == 2)
cout << " ";
}
template <class T>
void print(const vector<T>& v, int suc = 1) {
for (int i = 0; i < v.size(); ++i)
print(v[i], i == int(v.size()) - 1 ? suc : 2);
}
template <class T>
void show(T x) {
print(x, 1);
}
template <typename Head, typename... Tail>
void show(Head H, Tail... T) {
print(H, 2);
show(T...);
}
int topbit(int t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int botbit(int a) { return a == 0 ? 32 : __builtin_ctz(a); }
int botbit(ll a) { return a == 0 ? 64 : __builtin_ctzll(a); }
int popcount(int t) { return __builtin_popcount(t); }
int popcount(ll t) { return __builtin_popcountll(t); }
int bit_parity(int t) { return __builtin_parity(t); }
int bit_parity(ll t) { return __builtin_parityll(t); }
struct prepare_io {
prepare_io() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(10);
}
} prep_io;
#pragma endregion satashun
template <unsigned int MOD>
struct ModInt {
using uint = unsigned int;
using ull = unsigned long long;
using M = ModInt;
uint v;
ModInt(ll _v = 0) { set_norm(_v % MOD + MOD); }
M& set_norm(uint _v) { //[0, MOD * 2)->[0, MOD)
v = (_v < MOD) ? _v : _v - MOD;
return *this;
}
explicit operator bool() const { return v != 0; }
explicit operator int() const { return v; }
M operator+(const M& a) const { return M().set_norm(v + a.v); }
M operator-(const M& a) const { return M().set_norm(v + MOD - a.v); }
M operator*(const M& a) const { return M().set_norm(ull(v) * a.v % MOD); }
M operator/(const M& a) const { return *this * a.inv(); }
M& operator+=(const M& a) { return *this = *this + a; }
M& operator-=(const M& a) { return *this = *this - a; }
M& operator*=(const M& a) { return *this = *this * a; }
M& operator/=(const M& a) { return *this = *this / a; }
M operator-() const { return M() - *this; }
M& operator++(int) { return *this = *this + 1; }
M& operator--(int) { return *this = *this - 1; }
M pow(ll n) const {
if (n < 0) return inv().pow(-n);
M x = *this, res = 1;
while (n) {
if (n & 1) res *= x;
x *= x;
n >>= 1;
}
return res;
}
M inv() const {
ll a = v, b = MOD, p = 1, q = 0, t;
while (b != 0) {
t = a / b;
swap(a -= t * b, b);
swap(p -= t * q, q);
}
return M(p);
}
friend ostream& operator<<(ostream& os, const M& a) { return os << a.v; }
friend istream& operator>>(istream& in, M& x) {
ll v_;
in >> v_;
x = M(v_);
return in;
}
bool operator<(const M& r) const { return v < r.v; }
bool operator>(const M& r) const { return v < *this; }
bool operator<=(const M& r) const { return !(r < *this); }
bool operator>=(const M& r) const { return !(*this < r); }
bool operator==(const M& a) const { return v == a.v; }
bool operator!=(const M& a) const { return v != a.v; }
static uint get_mod() { return MOD; }
};
using Mint = ModInt<1000000007>;
// using Mint = ModInt<998244353>;
V<Mint> fact, ifact, inv;
VV<Mint> small_comb;
void mod_init() {
const int maxv = 2000010;
const int maxvv = 5000;
fact.resize(maxv);
ifact.resize(maxv);
inv.resize(maxv);
small_comb = make_vec<Mint>(maxvv, maxvv);
fact[0] = 1;
for (int i = 1; i < maxv; ++i) {
fact[i] = fact[i - 1] * i;
}
ifact[maxv - 1] = fact[maxv - 1].inv();
for (int i = maxv - 2; i >= 0; --i) {
ifact[i] = ifact[i + 1] * (i + 1);
}
for (int i = 1; i < maxv; ++i) {
inv[i] = ifact[i] * fact[i - 1];
}
for (int i = 0; i < maxvv; ++i) {
small_comb[i][0] = small_comb[i][i] = 1;
for (int j = 1; j < i; ++j) {
small_comb[i][j] = small_comb[i - 1][j] + small_comb[i - 1][j - 1];
}
}
}
Mint comb(int n, int r) {
if (n < 0 || r < 0 || r > n) return Mint(0);
if (n < small_comb.size()) return small_comb[n][r];
return fact[n] * ifact[r] * ifact[n - r];
}
Mint inv_comb(int n, int r) {
if (n < 0 || r < 0 || r > n) return Mint(0);
return ifact[n] * fact[r] * fact[n - r];
}
// O(k)
Mint comb_slow(ll n, ll k) {
if (n < 0 || k < 0 || k > n) return Mint(0);
Mint res = ifact[k];
for (int i = 0; i < k; ++i) {
res = res * (n - i);
}
return res;
}
// line up
// a 'o' + b 'x'
Mint comb2(int a, int b) {
if (a < 0 || b < 0) return 0;
return comb(a + b, a);
}
// divide a into b groups
Mint nhr(int a, int b) {
if (b == 0) return Mint(a == 0);
return comb(a + b - 1, a);
}
// O(p + log_p n)
Mint lucas(ll n, ll k, int p) {
if (n < 0 || k < 0 || k > n) return Mint(0);
Mint res = 1;
while (n > 0) {
res *= comb(n % p, k % p);
n /= p;
k /= p;
}
return res;
}
struct ModPrepare {
ModPrepare() { mod_init(); }
} prep_mod;
void slv() {
int H, W;
cin >> H >> W;
Mint ans;
for (int i = 0; i <= H; ++i) {
ans += comb(H, i) * (i % 2 ? -1 : 1) * (Mint(2).pow(H - i) - 1).pow(W);
}
show(ans);
}
int main() {
int cases = 1;
// cin >> cases;
rep(i, cases) slv();
return 0;
}
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