結果

問題 No.1627 三角形の成立
ユーザー heno239heno239
提出日時 2021-07-23 22:33:01
言語 C++17
(gcc 13.2.0 + boost 1.83.0)
結果
AC  
実行時間 826 ms / 1,000 ms
コード長 5,833 bytes
コンパイル時間 2,706 ms
コンパイル使用メモリ 157,116 KB
実行使用メモリ 29,484 KB
最終ジャッジ日時 2023-09-25 22:46:09
合計ジャッジ時間 10,438 ms
ジャッジサーバーID
（参考情報） 		judge11 / judge12
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
22,300 KB
testcase_01 AC 18 ms
22,344 KB
testcase_02 AC 17 ms
22,292 KB
testcase_03 AC 18 ms
22,264 KB
testcase_04 AC 17 ms
22,300 KB
testcase_05 AC 826 ms
29,208 KB
testcase_06 AC 548 ms
26,116 KB
testcase_07 AC 310 ms
24,312 KB
testcase_08 AC 534 ms
28,984 KB
testcase_09 AC 132 ms
23,252 KB
testcase_10 AC 637 ms
26,624 KB
testcase_11 AC 358 ms
27,136 KB
testcase_12 AC 746 ms
29,052 KB
testcase_13 AC 157 ms
24,044 KB
testcase_14 AC 771 ms
29,484 KB
testcase_15 AC 461 ms
25,856 KB
testcase_16 AC 114 ms
22,868 KB
testcase_17 AC 582 ms
26,816 KB
testcase_18 AC 760 ms
29,308 KB
testcase_19 AC 18 ms
22,256 KB
testcase_20 AC 17 ms
22,368 KB
testcase_21 AC 18 ms
22,272 KB
testcase_22 AC 18 ms
22,272 KB
testcase_23 AC 18 ms
22,332 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>
using namespace std;

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

typedef unsigned long long ul;
typedef unsigned int ui;
constexpr ll mod = 1000000007;
const ll INF = mod * mod;
typedef pair<int, int>P;
#define stop char nyaa;cin>>nyaa;
#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;
typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-10;
const ld pi = acosl(-1.0);

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;
	ll res = 1;
	while (n) {
		if (n & 1)res = res * x % m;
		x = x * x % m; n >>= 1;
	}
	return res;
}
struct modint {
	ll n;
	modint() :n(0) { ; }
	modint(ll m) :n(m) {
		if (n >= mod)n %= mod;
		else if (n < 0)n = (n % mod + mod) % mod;
	}
	operator int() { return 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 -= mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += 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 = 1000000;
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];
}

modint comb3(modint n) {
	modint res = n;
	res *= n - (modint)1;
	res *= n - (modint)2;
	res *= (1 + mod) / 6;
	return res;
}

/*modint mem[1 << 18];
bool used[1 << 18];
modint calc(int len) {
	if (used[len])return mem[len];
	used[len] = true;
	if (len == 0)return mem[len] = 0;
	for (int i = 1; i <= len; i++) {
		int d = len / i;
		int r = len % i;
		modint s = (modint)r * comb3(d + 1);
		s += (modint)(i - r) * comb3(d);
		mem[len] += s;
	}
	return mem[len];
}*/

modint mem[1 << 18];
modint calc1(int a, int b) {
	if (a > b)swap(a, b);
	modint res = (modint)2 * mem[a] + (modint)(b - a + 1) * comb3(a);
	//cout << "?? " <<a<<" "<<b<<" "<< res << "\n";
	return res;
}
vector<P> makec(int len) {
	vector<P> vp;
	for (int c = 1; c <= len; c++) {
		int d = len / c;
		int r = len % c;
		if (r > 0)vp.push_back({ d + 1,r });
		vp.push_back({ d,c - r });
	}
	sort(all(vp));
	vector<P> res;
	rep(i, vp.size()) {
		int sum = vp[i].second;
		while (i + 1 < vp.size() && vp[i].first == vp[i + 1].first) {
			i++;
			sum += vp[i].second;
		}
		res.push_back({ vp[i].first,sum });
	}
	return res;
}
map<P, modint> mp;
modint calc2(int n, int m) {
	if (n > m)swap(n, m);
	if (mp.find({ n,m }) != mp.end())return mp[{n, m}];
	vector<P> cn = makec(n);
	vector<P> cm = makec(m);
	modint res = 0;
	rep(i, cn.size())rep(j, cm.size()) {
		modint val = calc1(cn[i].first, cm[j].first);
		modint num = (modint)cn[i].second * (modint)cm[j].second;
		res += val * num;
	}
	return mp[{n, m}]=res;
}

const int mn = (1 << 18);
int meb[1 << 18];
bool isp[1 << 18];
void init() {
	fill(isp + 2, isp + mn, true);
	fill(meb + 1, meb + mn, 1);
	for (int i = 2; i < mn; i++) {
		if (!isp[i])continue;
		meb[i] *= -1;
		for (int j = 2 * i; j < mn; j += i) {
			meb[j] *= -1;
			isp[j] = false;
			if ((j / i) % i == 0)meb[j] = 0;
		}
	}
	rep(i, mn - 1) {
		mem[i + 1] = mem[i] + comb3(i);
	}
}
void solve() {
	ll n, m; cin >> n >> m;
	modint ans = 0;
	for (int g = 1; g <= min(n, m); g++) {
		if (meb[g] == 0)continue;
		int d1 = n / g;
		int r1 = n % g;
		int d2 = m / g;
		int r2 = m % g;
		modint dm = (ll)r1 * r2;
		modint csum = 0;
		if (r1 > 0 && r2 > 0)csum += dm * calc2(d1 + 1, d2 + 1);
		dm = (ll)r1 * (g - r2);
		if (r1 > 0)csum += (modint)dm * calc2(d1 + 1, d2);
		dm = (ll)(g - r1) * r2;
		if (r2 > 0)csum += (modint)dm * calc2(d1, d2 + 1);
		dm = (ll)(g - r1) * (g - r2);
		csum += (modint)dm * calc2(d1, d2);
		ans += csum * (modint)meb[g];
		//cout << g << " " << csum << " " << meb[g] << "\n";
	}
	ans *= 2;
	//cout << "? " << ans << "\n";
	modint al = comb3(n * m) - (modint)m * comb3(n) - (modint)n * comb3(m);
	//cout << al << "\n";
	ans = comb3(n * m) - (modint)m * comb3(n) - (modint)n * comb3(m) - ans;
	cout << ans << "\n";
}

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