#831042 (C++17) No.2181 LRM Question 2

提出ソース

結果

問題	No.2181 LRM Question 2
ユーザー	heno239
提出日時	2023-01-06 22:58:29
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	205 ms / 2,000 ms
コード長	8,418 bytes
コンパイル時間	2,048 ms
コンパイル使用メモリ	154,096 KB
実行使用メモリ	11,852 KB
最終ジャッジ日時	2024-05-07 22:41:29
合計ジャッジ時間	4,410 ms
ジャッジサーバーID （参考情報）	judge4 / judge2

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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	7 ms 11,648 KB
testcase_01	AC	7 ms 11,648 KB
testcase_02	AC	147 ms 11,776 KB
testcase_03	AC	8 ms 11,720 KB
testcase_04	AC	8 ms 11,648 KB
testcase_05	AC	8 ms 11,848 KB
testcase_06	AC	7 ms 11,648 KB
testcase_07	AC	7 ms 11,648 KB
testcase_08	AC	199 ms 11,776 KB
testcase_09	AC	131 ms 11,776 KB
testcase_10	AC	205 ms 11,852 KB
testcase_11	AC	205 ms 11,852 KB
testcase_12	AC	196 ms 11,776 KB
testcase_13	AC	9 ms 11,776 KB
testcase_14	AC	41 ms 11,776 KB
testcase_15	AC	9 ms 11,776 KB
testcase_16	AC	199 ms 11,776 KB
testcase_17	AC	10 ms 11,716 KB
testcase_18	AC	10 ms 11,720 KB
testcase_19	AC	11 ms 11,776 KB
testcase_20	AC	16 ms 11,776 KB
testcase_21	AC	40 ms 11,776 KB
testcase_22	AC	12 ms 11,776 KB
testcase_23	AC	7 ms 11,776 KB
testcase_24	AC	7 ms 11,776 KB
testcase_25	AC	8 ms 11,848 KB

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ソースコード

raw source code

#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 << 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;
}
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 };
//-----------------------------------------

ll calc(ll n) {
	ll sum = 0;
	rep1(i, n - 1) {
		ll pro = 1;
		rep1(j, i) {
			pro *= n - j + 1;
			pro *= n - j + 1;
		}
		Rep1(j, i + 1, n) {
			pro *= j;
			pro *= j;
		}
		sum += pro;
	}
	ll pro = 1;
	rep1(i, n)pro *= i;
	sum /= pro;
	sum /= pro;
	return sum;
}
void expr() {
	rep1(n, 20) {
		cout << n << " " << calc(n) << "\n";
	}
}

//x,yがax+by=gcd(a,b)の解になる
ll extgcd(ll a, ll b, ll& x, ll& y) {
	ll d = a;
	if (b != 0) {
		d = extgcd(b, a % b, y, x);
		y -= (a / b) * x;
	}
	else {
		x = 1; y = 0;
	}
	return d;
}
//aのmod mでの逆元を求める
ll mod_inverse(ll a, ll m) {
	ll x, y;
	extgcd(a, m, x, y);
	return (m + x % m) % m;
}

ll f(ll n, ll p) {
	ll res = 0;
	while (n) {
		res += n / p; n /= p;
	}
	return res;
}
//mod p^q
ll calc(ll le, ll ri, ll p, ll q) {
	ll pp = 1; rep(i, q)pp *= p;
	//ll res = 0;
	ll curv = 1, curc = 0;
	auto calc_val = [&]() {
		assert(curv < pp);
		ll res = curv;
		for (ll i = 0; i < curc; i++) {
			res = res * p % pp;
			if (res == 0)break;
		}
		return res;
	};
	//binomial[2*le,le]
	curc = f(2 * le, p) - 2 * f(le, p);
	
	rep(i, pp) {
		if (i % p == 0)continue;
		ll cnt = 0;
		ll s = 2 * le;
		while (i <= s) {
			cnt += (s - i) / pp + 1;
			s /= p;
		}
		s = le;
		while (i <= s) {
			cnt -= (s - i) / pp + 1;
			cnt -= (s - i) / pp + 1;
			s /= p;
		}
		ll adv = i;
		if (cnt < 0) {
			adv = mod_inverse(i, pp);
			cnt *= -1;
		}
		curv = curv * mod_pow(adv, cnt, pp) % pp;
	}
	/*rep(i, pp) {
		if (i == 0)continue;
		ll adv = i;
		while (adv % p == 0)adv /= p;
		adv %= pp;
		ll cnt = 0;
		if (2 * le >= i) {
			cnt += (2*le - i) / pp + 1;
		}
		if (le >= i) {
			cnt -= (le - i) / pp + 1;
			cnt -= (le - i) / pp + 1;
		}
		if (cnt < 0) {
			adv = mod_inverse(adv, pp);
			cnt *= -1;
		}
		curv = curv * mod_pow(adv, cnt, pp) % pp;
	}*/
	auto add = [&](ll x) {
		while (x % p == 0) {
			x /= p; curc++;
		}
		x %= pp;
		assert(x% p);
		assert(x < pp);
		curv = curv * x % pp;
	};
	auto add_b = [&](ll x) {
		while (x % p == 0) {
			x /= p; curc--;
		}
		x %= pp;
		x = mod_inverse(x, pp);
		assert(x% p);
		assert(x < pp);
		curv = curv * x % pp;
	};
	assert(curv < pp);
	//if(p==5)cout << "! " << curv << "\n";
	ll res = calc_val();
	for (ll i = le + 1; i <= ri; i++) {
		//cout << res <<" "<<curv<<" "<<curc<< "\n";
		add(2 * i - 1);
		add(2 * i);
		add_b(i);
		add_b(i);
		res += calc_val();
		res %= pp;
		/*if (curv == 0&&p==5) {
			cout << "!? " << i << "\n";
		}
		if (curc<q) {
			cout << "!! "<<p<<" "<<q<<" "<<i<<" "<<curc<<" "<<curv<<"\n";
			cout << f(2 * i, p) << " " << 2 * f(i, p) << "\n";
			cout << calc_val() << "\n";
		}*/
	}
	return res;
}
void solve() {
	ll l, r, m; cin >> l >> r >> m;
	vector<LP> ps;
	for (ll i = 2; i <= m; i++) {
		if (m % i == 0) {
			int cnt = 0;
			while (m % i == 0) {
				m /= i;
				cnt++;
			}
			ps.push_back({ i,cnt });
		}
	}
	ll ans = 0;
	ll ansm = 1;
	rep(i, ps.size()) {
		ll p = ps[i].first;
		ll q = ps[i].second;
		ll pp = 1; rep(i, q)pp *= p;
		ll val = calc(l, r, p, q);
		//cout << "?? " << p << " " << q << " " << val << "\n";
		//= val mod pp
		while (ans % pp != val) {
			ans += ansm;
		}
		ansm *= pp;
		//cout << ans << " " << ansm << "\n";
	}

	ans -= 2 * (r - l + 1);
	while (ans < 0)ans += ansm;
	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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テストケース

ソースコード