結果

問題 No.829 成長関数インフレ中
ユーザー heno239heno239
提出日時 2023-04-18 06:23:23
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 1,560 ms / 2,000 ms
コード長 11,508 bytes
コンパイル時間 3,035 ms
コンパイル使用メモリ 180,116 KB
実行使用メモリ 36,100 KB
最終ジャッジ日時 2024-04-21 05:44:31
合計ジャッジ時間 10,465 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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 19 ms
11,776 KB
testcase_01 AC 20 ms
11,776 KB
testcase_02 AC 18 ms
11,848 KB
testcase_03 AC 19 ms
11,844 KB
testcase_04 AC 19 ms
11,776 KB
testcase_05 AC 18 ms
11,848 KB
testcase_06 AC 18 ms
11,776 KB
testcase_07 AC 18 ms
11,776 KB
testcase_08 AC 18 ms
11,776 KB
testcase_09 AC 18 ms
11,904 KB
testcase_10 AC 19 ms
11,904 KB
testcase_11 AC 18 ms
11,848 KB
testcase_12 AC 33 ms
12,364 KB
testcase_13 AC 19 ms
11,844 KB
testcase_14 AC 29 ms
12,104 KB
testcase_15 AC 299 ms
17,368 KB
testcase_16 AC 648 ms
23,532 KB
testcase_17 AC 1,012 ms
25,016 KB
testcase_18 AC 1,448 ms
34,972 KB
testcase_19 AC 1,097 ms
25,788 KB
testcase_20 AC 1,560 ms
36,100 KB
testcase_21 AC 27 ms
12,032 KB
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;
//ll mod = 1;
//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;

using ld = long double;
typedef pair<ld, ld> LDP;
const ld eps = 1e-10;
const ld pi = acosl(-1.0);

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>
vector<T> vmerge(vector<T>& a, vector<T>& b) {
	vector<T> res;
	int ida = 0, idb = 0;
	while (ida < a.size() || idb < b.size()) {
		if (idb == b.size()) {
			res.push_back(a[ida]); ida++;
		}
		else if (ida == a.size()) {
			res.push_back(b[idb]); idb++;
		}
		else {
			if (a[ida] < b[idb]) {
				res.push_back(a[ida]); ida++;
			}
			else {
				res.push_back(b[idb]); idb++;
			}
		}
	}
	return res;
}
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 << 20;
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;
}
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 };

//-----------------------------------------

int bsf(int x) {
	int res = 0;
	while (!(x & 1)) {
		res++; x >>= 1;
	}
	return res;
}
int ceil_pow2(int n) {
	int x = 0;
	while ((1 << x) < n) x++;
	return x;
}
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;
}
const array<ll, 3> ms = { 469762049,167772161,595591169 };
const array<ll, 3> proots = { get_premitive_root(469762049),get_premitive_root(167772161),get_premitive_root(595591169) };
using poly = vector<ll>;
using polys = array<poly, 3>;
void butterfly(polys& a) {
	int n = int(a[0].size());
	array<ll, 3> gs = proots;
	int h = ceil_pow2(n);

	static bool first = true;
	static ll sum_e[3][30];  // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
	if (first) {
		first = false;
		ll es[3][30], ies[3][30];  // es[i]^(2^(2+i)) == 1
		int cnt2[3];
		rep(i, 3)cnt2[i] = bsf(ms[i] - 1);
		ll e[3];
		rep(i, 3)e[i] = mod_pow(gs[i], (ms[i] - 1) >> cnt2[i], ms[i]);
		ll ie[3];
		rep(i, 3)ie[i] = mod_pow(e[i], ms[i] - 2, ms[i]);
		rep(j, 3) {
			for (int i = cnt2[j]; i >= 2; i--) {
				// e^(2^i) == 1
				es[j][i - 2] = e[j];
				ies[j][i - 2] = ie[j];
				e[j] *= e[j]; e[j] %= ms[j];
				ie[j] *= ie[j]; ie[j] %= ms[j];
			}
		}
		rep(j, 3) {
			ll now = 1;
			for (int i = 0; i < cnt2[j] - 2; i++) {
				sum_e[j][i] = es[j][i] * now % ms[j];
				now *= ies[j][i]; now %= ms[j];
			}
		}
	}
	for (int ph = 1; ph <= h; ph++) {
		int w = 1 << (ph - 1), p = 1 << (h - ph);
		ll now[3] = { 1,1,1 };
		for (int s = 0; s < w; s++) {
			int offset = s << (h - ph + 1);
			for (int i = 0; i < p; i++) {
				rep(j, 3) {
					auto l = a[j][i + offset];
					auto r = a[j][i + offset + p] * now[j] % ms[j];
					a[j][i + offset] = l + r; if (a[j][i + offset] >= ms[j])a[j][i + offset] -= ms[j];
					a[j][i + offset + p] = l - r; if (a[j][i + offset + p] < 0)a[j][i + offset + p] += ms[j];
				}
			}
			rep(j, 3) {
				now[j] *= sum_e[j][bsf(~(unsigned int)(s))];
				now[j] %= ms[j];
			}
		}
	}
}
void butterfly_inv(polys& a) {
	int n = int(a[0].size());
	array<ll, 3> gs = proots;
	int h = ceil_pow2(n);

	static bool first = true;
	static ll sum_ie[3][30];  // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
	if (first) {
		first = false;
		ll es[3][30], ies[3][30];  // es[i]^(2^(2+i)) == 1
		int cnt2[3];
		rep(i, 3)cnt2[i] = bsf(ms[i] - 1);
		ll e[3];
		rep(i, 3)e[i] = mod_pow(gs[i], (ms[i] - 1) >> cnt2[i], ms[i]);
		ll ie[3];
		rep(i, 3)ie[i] = mod_pow(e[i], ms[i] - 2, ms[i]);
		rep(j, 3) {
			for (int i = cnt2[j]; i >= 2; i--) {
				// e^(2^i) == 1
				es[j][i - 2] = e[j];
				ies[j][i - 2] = ie[j];
				e[j] *= e[j]; e[j] %= ms[j];
				ie[j] *= ie[j]; ie[j] %= ms[j];
			}
		}
		rep(j, 3) {
			ll now = 1;
			for (int i = 0; i < cnt2[j] - 2; i++) {
				sum_ie[j][i] = ies[j][i] * now % ms[j];
				now *= es[j][i]; now %= ms[j];
			}
		}
	}
	for (int ph = h; ph >= 1; ph--) {
		int w = 1 << (ph - 1), p = 1 << (h - ph);
		ll inow[3] = { 1,1,1 };
		for (int s = 0; s < w; s++) {
			int offset = s << (h - ph + 1);
			for (int i = 0; i < p; i++) {
				rep(j, 3) {
					auto l = a[j][i + offset];
					auto r = a[j][i + offset + p];
					a[j][i + offset] = l + r; if (a[j][i + offset] >= ms[j])a[j][i + offset] -= ms[j];
					a[j][i + offset + p] = (ms[j] + l - r) * inow[j] % ms[j];
				}
			}
			rep(j, 3) {
				inow[j] *= sum_ie[j][bsf(~(unsigned int)(s))];
				inow[j] %= ms[j];
			}
		}
	}
}


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) {
	int n = g.size();
	int m = h.size();
	if (n == 0 || m == 0)return {};
	if (min(g.size(), h.size()) < 60) {
		poly res(g.size() + h.size() - 1);
		rep(i, g.size())rep(j, h.size()) {
			res[i + j] += g[i] * h[j];
			res[i + j] %= p;
		}
		return res;
	}
	int z = 1 << ceil_pow2(n + m - 1);
	g.resize(z); h.resize(z);
	polys gs, hs;
	rep(j, 3) {
		gs[j].resize(z);
		hs[j].resize(z);
		rep(i, z) {
			gs[j][i] = g[i] % ms[j];
			hs[j][i] = h[i] % ms[j];
		}
	}
	butterfly(gs);
	butterfly(hs);
	rep(j, 3)rep(i, z) {
		(gs[j][i] *= hs[j][i]) %= ms[j];
	}
	butterfly_inv(gs);
	rep(j, 3) {
		gs[j].resize(n + m - 1);
		ll iz = mod_pow(z, ms[j] - 2, ms[j]);
		rep(i, n + m - 1) {
			(gs[j][i] *= iz) %= ms[j];
		}
	}
	poly res(n + m - 1);
	rep(i, n + m - 1) {
		res[i] = calc(gs[0][i], gs[1][i], gs[2][i], p);
	}
	return res;
}
void solve(){
	int n, b; cin >> n >> b;
	vector<int> s(n);
	rep(i, n)cin >> s[i];
	sort(all(s));
	vector<int> cs;
	rep(i, n) {
		int c = 1; while (i + 1 < n && s[i] == s[i + 1]) {
			i++; c++;
		}
		cs.push_back(c);
	}
	vector<poly> vs;
	int presum = 0;
	per(i, cs.size()) {
		modint c01 = comb(presum + cs[i], cs[i]);
		modint c0 = comb(presum + cs[i] - 1, presum - 1);
		modint c1 = c01 - c0;
		poly cur = { c0,c1 };
		//coutarray(cur);
		vs.push_back(cur);
		presum += cs[i];
	}
	while (vs.size() > 1) {
		vector<poly> nvs;
		for (int i = 0; i + 1 < vs.size(); i += 2) {
			poly cur = multiply(vs[i], vs[i + 1],mod);
			nvs.push_back(cur);
		}
		if (vs.size() % 2)nvs.push_back(vs.back());
		swap(vs, nvs);
	}
	modint ans = 0;
	rep(i, vs[0].size()) {
		modint val = (modint)i * (modint)mod_pow(b, i);
		val *= vs[0][i];
		ans += val;
	}
	rep(i, cs.size())ans *= fact[cs[i]];
	cout << ans << "\n";
}



signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(12);
	init_f();
	//init();
	//while(true)
	//expr();
	//int t; cin >> t; rep(i, t)
	solve();
	return 0;
}
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