結果

問題 No.940 ワープ　ε=ε=ε=ε=ε=│;p>д＜│
ユーザー heno239heno239
提出日時 2023-01-26 02:58:39
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
TLE  
実行時間 -
コード長 12,527 bytes
コンパイル時間 3,153 ms
コンパイル使用メモリ 181,804 KB
実行使用メモリ 118,596 KB
最終ジャッジ日時 2024-06-27 02:48:18
合計ジャッジ時間 18,995 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge5
このコードへのチャレンジ
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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 AC 72 ms
41,728 KB
testcase_01 AC 72 ms
36,352 KB
testcase_02 AC 73 ms
36,424 KB
testcase_03 AC 186 ms
37,448 KB
testcase_04 AC 73 ms
36,424 KB
testcase_05 AC 125 ms
36,660 KB
testcase_06 AC 98 ms
36,680 KB
testcase_07 AC 98 ms
36,552 KB
testcase_08 AC 86 ms
36,608 KB
testcase_09 AC 98 ms
36,636 KB
testcase_10 AC 97 ms
36,548 KB
testcase_11 AC 85 ms
36,552 KB
testcase_12 AC 125 ms
36,700 KB
testcase_13 AC 97 ms
36,636 KB
testcase_14 AC 78 ms
36,552 KB
testcase_15 AC 2,367 ms
56,960 KB
testcase_16 AC 4,972 ms
82,524 KB
testcase_17 TLE -
testcase_18 -- -
testcase_19 -- -
testcase_20 -- -
testcase_21 -- -
testcase_22 -- -
testcase_23 -- -
testcase_24 -- -
testcase_25 -- -
testcase_26 -- -
権限があれば一括ダウンロードができます

ソースコード

diff # 

#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<unordered_set>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
#include<array>
#include<chrono>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
//constexpr ll mod = 998244353;
constexpr ll mod = 1000000007;
const ll INF = mod * mod;
typedef pair<int, int>P;

#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;

template<typename T>
void chmin(T& a, T b) {
	a = min(a, b);
}
template<typename T>
void chmax(T& a, T b) {
	a = max(a, b);
}
template<typename T>
void cinarray(vector<T>& v) {
	rep(i, v.size())cin >> v[i];
}
template<typename T>
void coutarray(vector<T>& v) {
	rep(i, v.size()) {
		if (i > 0)cout << " "; cout << v[i];
	}
	cout << "\n";
}
ll mod_pow(ll x, ll n, ll m = mod) {
	if (n < 0) {
		ll res = mod_pow(x, -n, m);
		return mod_pow(res, m - 2, m);
	}
	if (abs(x) >= m)x %= m;
	if (x < 0)x += m;
	//if (x == 0)return 0;
	ll res = 1;
	while (n) {
		if (n & 1)res = res * x % m;
		x = x * x % m; n >>= 1;
	}
	return res;
}
//mod should be <2^31
struct modint {
	int n;
	modint() :n(0) { ; }
	modint(ll m) {
		if (m < 0 || mod <= m) {
			m %= mod; if (m < 0)m += mod;
		}
		n = m;
	}
	operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
bool operator<(modint a, modint b) { return a.n < b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= (int)mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += (int)mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, ll n) {
	if (n == 0)return modint(1);
	modint res = (a * a) ^ (n / 2);
	if (n % 2)res = res * a;
	return res;
}

ll inv(ll a, ll p) {
	return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }
modint operator/=(modint& a, modint b) { a = a / b; return a; }
const int max_n = 1 << 22;
modint fact[max_n], factinv[max_n];
void init_f() {
	fact[0] = modint(1);
	for (int i = 0; i < max_n - 1; i++) {
		fact[i + 1] = fact[i] * modint(i + 1);
	}
	factinv[max_n - 1] = modint(1) / fact[max_n - 1];
	for (int i = max_n - 2; i >= 0; i--) {
		factinv[i] = factinv[i + 1] * modint(i + 1);
	}
}
modint comb(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[b] * factinv[a - b];
}
modint combP(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[a - b];
}

ll gcd(ll a, ll b) {
	a = abs(a); b = abs(b);
	if (a < b)swap(a, b);
	while (b) {
		ll r = a % b; a = b; b = r;
	}
	return a;
}
using ld = long double;
//typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-10;
const ld pi = acosl(-1.0);
template<typename T>
void addv(vector<T>& v, int loc, T val) {
	if (loc >= v.size())v.resize(loc + 1, 0);
	v[loc] += val;
}
/*const int mn = 2000005;
bool isp[mn];
vector<int> ps;
void init() {
	fill(isp + 2, isp + mn, true);
	for (int i = 2; i < mn; i++) {
		if (!isp[i])continue;
		ps.push_back(i);
		for (int j = 2 * i; j < mn; j += i) {
			isp[j] = false;
		}
	}
}*/

//[,val)
template<typename T>
auto prev_itr(set<T>& st, T val) {
	auto res = st.lower_bound(val);
	if (res == st.begin())return st.end();
	res--; return res;
}

//[val,)
template<typename T>
auto next_itr(set<T>& st, T val) {
	auto res = st.lower_bound(val);
	return res;
}
using mP = pair<modint, modint>;
mP operator+(mP a, mP b) {
	return { a.first + b.first,a.second + b.second };
}
mP operator+=(mP& a, mP b) {
	a = a + b; return a;
}
mP operator-(mP a, mP b) {
	return { a.first - b.first,a.second - b.second };
}
mP operator-=(mP& a, mP b) {
	a = a - b; return a;
}
LP operator+(LP a, LP b) {
	return { a.first + b.first,a.second + b.second };
}
LP operator+=(LP& a, LP b) {
	a = a + b; return a;
}
LP operator-(LP a, LP b) {
	return { a.first - b.first,a.second - b.second };
}
LP operator-=(LP& a, LP b) {
	a = a - b; return a;
}

mt19937 mt(time(0));

const string drul = "DRUL";
string senw = "SENW";
//DRUL,or SENW
int dx[4] = { 1,0,-1,0 };
int dy[4] = { 0,1,0,-1 };
//-----------------------------------------


void expr() {
	for (int n = 1; n <= 10; n++) {
		vector<modint> f(n + 1);
		vector<modint> res(n + 1);
		for (int i = n; i >= 0; i--) {
			modint coef = (modint)1 - f[i];
			res[i] = coef;
			rep(j, i + 1) {
				f[j] += coef * comb(i,j);
			}
		}
		rep(i, res.size()) {
			if ((n + i) % 2)res[i] *= -1;
		}
		res.erase(res.begin());
		coutarray(res);
	}
}




int get_premitive_root(const ll& p) {
	int primitive_root = 0;
	if (!primitive_root) {
		primitive_root = [&]() {
			set<int> fac;
			int v = p - 1;
			for (ll 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 < p; g++) {
				bool ok = true;
				for (auto i : fac) if (mod_pow(g, (p - 1) / i, p) == 1) { ok = false; break; }
				if (ok) return g;
			}
			return -1;
		}();
	}
	return primitive_root;
}


typedef vector <ll> poly;
void dft(poly& f, const ll& p, const int& proot, bool inverse = false) {
	int n = f.size(); if (n == 1)return;

	poly w{ 1 }, iw{ 1 };
	for (int m = w.size(); m < n / 2; m *= 2) {
		ll dw = mod_pow(proot, (p - 1) / (4 * m), p), dwinv = mod_pow(dw, p - 2, p);
		w.resize(m * 2); iw.resize(m * 2);
		for (int i = 0; i < m; i++)w[m + i] = w[i] * dw % p, iw[m + i] = iw[i] * dwinv % p;
	}
	if (!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++) {
					ll x = f[i], y = f[i + m] * w[k] % p;
					f[i] = x + y, f[i + m] = x - y;
					if (f[i] >= p)f[i] -= p;
					if (f[i + m] < 0)f[i + m] += p;
				}
			}
		}
	}
	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++) {
					ll x = f[i], y = f[i + m];
					f[i] = x + y, f[i + m] = (x - y) * iw[k] % p;
					if (f[i] >= p)f[i] -= p;
					if (f[i + m] < 0)f[i + m] += p;
				}
			}
		}
		ll n_inv = mod_pow(n, p - 2, p);
		for (ll& v : f)(v *= n_inv) %= p;
	}
}


poly multi(poly g, poly h, const ll& p, int n) {
	const int proot = get_premitive_root(p);
	dft(g, p, proot, false);
	dft(h, p, proot, false);
	poly f(n);
	rep(i, n) {
		f[i] = g[i] * h[i] % p;
	}
	dft(f, p, proot, true);
	return f;
}

constexpr ll m0 = 469762049;
constexpr ll m1 = 167772161;
constexpr ll m2 = 595591169;
const ll inv01 = mod_pow(m0, m1 - 2, m1);
const ll inv012 = mod_pow(m0 * m1, m2 - 2, m2);

ll calc(ll& a, ll& b, ll& c, const ll& p) {
	ll res = 0;
	ll x1 = a;
	ll x2 = (b - x1) * inv01;
	x2 %= m1; if (x2 < 0)x2 += m1;
	ll x3 = (c - x1 - x2 * m0) % m2 * inv012;
	x3 %= m2; if (x3 < 0)x3 += m2;
	res = x1 + x2 * m0 % p + x3 * m0 % p * m1;
	return res % p;
}
poly multiply(poly g, poly h, const ll& p=mod) {

	int resz = g.size() + h.size() - 1;

	int n = 1;
	int pi = 0, qi = 0;
	rep(i, g.size())if (g[i])pi = i;
	rep(i, h.size())if (h[i])qi = i;
	int sz = pi + qi + 2;
	while (n < sz)n *= 2;
	g.resize(n); h.resize(n);

	poly vp[3];
	vp[0] = multi(g, h, m0, n);
	vp[1] = multi(g, h, m1, n);
	vp[2] = multi(g, h, m2, n);
	poly res(resz);
	rep(i, res.size()) {
		ll a, b, c;
		if (i < vp[0].size())a = vp[0][i];
		else a = 0;
		if (i < vp[1].size())b = vp[1][i];
		else b = 0;
		if (i < vp[2].size())c = vp[2][i];
		else c = 0;
		res[i] = calc(a, b, c, p);
	}
	return res;
}


struct FormalPowerSeries :vector<modint> {
	using vector<modint>::vector;
	using fps = FormalPowerSeries;
	void shrink() {
		while (this->size() && this->back() == (modint)0)this->pop_back();
	}

	fps operator+(const fps& r)const { return fps(*this) += r; }
	fps operator+(const modint& v)const { return fps(*this) += v; }
	fps operator-(const fps& r)const { return fps(*this) -= r; }
	fps operator-(const modint& v)const { return fps(*this) -= v; }
	fps operator*(const fps& r)const { return fps(*this) *= r; }
	fps operator*(const modint& v)const { return fps(*this) *= v; }


	fps& operator+=(const fps& r) {
		if (r.size() > this->size())this->resize(r.size());
		rep(i, r.size())(*this)[i] += r[i];
		shrink();
		return *this;
	}
	fps& operator+=(const modint& v) {
		if (this->empty())this->resize(1);
		(*this)[0] += v;
		shrink();
		return *this;
	}
	fps& operator-=(const fps& r) {
		if (r.size() > this->size())this->resize(r.size());
		rep(i, r.size())(*this)[i] -= r[i];
		shrink();
		return *this;
	}
	fps& operator-=(const modint& v) {
		if (this->empty())this->resize(1);
		(*this)[0] -= v;
		shrink();
		return *this;
	}
	fps& operator*=(const fps& r) {
		if (this->empty() || r.empty())this->clear();
		else {
			auto& cop = *this;
			poly p(cop.size()); rep(i, cop.size())p[i] = cop[i];
			poly q(r.size()); rep(i, r.size()) {
				modint x = r[i]; q[i] = x;
			}
			poly ret = multiply(p,q);
			*this = fps(all(ret));
		}
		shrink();
		return *this;
	}
	fps& operator*=(const modint& v) {
		for (auto& x : (*this))x *= v;
		shrink();
		return *this;
	}
	fps operator-()const {
		fps ret = *this;
		for (auto& v : ret)v = -v;
		return ret;
	}

	modint sub(modint x) {
		modint t = 1;
		modint res = 0;
		rep(i, (*this).size()) {
			res += t * (*this)[i];
			t *= x;
		}
		return res;
	}
	fps pre(int sz)const {
		fps ret(this->begin(), this->begin() + min((int)this->size(), sz));
		ret.shrink();
		return ret;
	}
	fps integral() const {
		const int n = (int)this->size();
		fps ret(n + 1);
		ret[0] = 0;
		for (int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / (modint)(i + 1);
		return ret;
	}
	fps inv(int deg = -1)const {
		const int n = this->size();
		if (deg == -1)deg = n;
		fps ret({ (modint)1 / (*this)[0] });
		for (int i = 1; i < deg; i <<= 1) {
			ret = (ret + ret - ret * ret * pre(i << 1)).pre(i << 1);
		}
		ret = ret.pre(deg);
		ret.shrink();
		return ret;
	}
	fps diff() const {
		const int n = (int)this->size();
		fps ret(max(0, n - 1));
		for (int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * (modint)i;
		return ret;
	}
	// F(0) must be 1
	fps 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();
	}
	// F(0) must be 0
	fps exp(int deg = -1)const {
		assert((*this)[0] == 0);
		const int n = (int)this->size();
		if (deg == -1)deg = n;
		fps ret = { 1 };
		for (int i = 1; i < deg; i <<= 1) {
			ret = (ret * (pre(i << 1) + 1 - ret.log(i << 1))).pre(i << 1);
		}
		//cout << "!!!! " << ret.size() << "\n";
		return ret.pre(deg);
	}
	fps div(fps g) {
		assert(g.size() && g.back() != (modint)0);
		fps f = *this;
		if (f.size() < g.size())return {};
		int dif = f.size() - g.size();
		reverse(all(f));
		reverse(all(g));
		g = g.inv(dif + 1);
		fps fg = f * g;
		fps ret(dif + 1);
		rep(i, fg.size()) {
			int id = i - dif;
			if (-dif <= id && id <= 0) {
				ret[-id] = fg[i];
			}
		}
		return ret;
	}
	fps divr(fps g) {
		fps ret = (*this) - g * (*this).div(g);
		ret.shrink();
		return ret;
	}
};
using fps = FormalPowerSeries;




void solve() {
	int x, y, z; cin >> x >> y >> z;
	if (x == 0 && y == 0 && z == 0) {
		cout << 1 << "\n"; return;
	}
	int n = x + y + z;
	fps f(n + 1);
	rep1(i, n) {
		f[i] = comb(x + i - 1, x) * comb(y + i - 1, y) * comb(z + i - 1, z);
	}
	//coutarray(f);
	fps g(n + 1);
	rep(i, n + 1) {
		g[i] = factinv[i];
	}
	//coutarray(g);
	g = g.inv();
	//coutarray(g);
	rep(i, n + 1)f[i] *= factinv[i];
	fps h = f * g;
	//coutarray(h);
	h.resize(n + 1);
	rep(i, n + 1) {
		h[i] *= fact[i];
	}
	modint ans = 0;
	rep(i, n + 1)ans += h[i];
	cout << ans << "\n";
}

signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(10);
	init_f();
	//init();
	//expr();
	//while(true)
	//int t; cin >> t; rep(i, t)
		solve();
	return 0;
}
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