結果
| 問題 |
No.1627 三角形の成立
|
| コンテスト | |
| ユーザー |
 heno239
|
| 提出日時 | 2021-07-23 22:33:01 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 726 ms / 1,000 ms |
| コード長 | 5,833 bytes |
| コンパイル時間 | 1,989 ms |
| コンパイル使用メモリ | 161,092 KB |
| 最終ジャッジ日時 | 2025-01-23 08:17:55 |
|
ジャッジサーバーID （参考情報） |
judge4 / judge1 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 22 |
ソースコード
#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;
}