結果

問題 No.1626 三角形の構築
コンテスト
ユーザー heno239
提出日時 2021-07-24 00:13:04
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,895 ms / 2,000 ms
コード長 4,635 bytes
コンパイル時間 2,291 ms
コンパイル使用メモリ 169,044 KB
最終ジャッジ日時 2025-01-23 09:08:26
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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ファイルパターン 結果
sample AC * 1
other AC * 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>
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];
}

int gcd(int a, int b) {
	if (a < b)swap(a, b);
	while (b) {
		int r = a % b; a = b; b = r;
	}
	return a;
}
void solve() {
	ul s, t; cin >> s >> t;
	ul ss = s * s * 16;
	if (ss % t) {
		cout << 0 << "\n"; return;
	}
	ss /= t;
	vector<ul> ds;
	rep1(d, 60000) {
		if (4 * s % d == 0) {
			ds.push_back(d);
			ds.push_back(4 * s / d);
		}
	}
	sort(all(ds)); ds.erase(unique(all(ds)), ds.end());
	vector<ul> dds;
	rep(i, ds.size()) {
		Rep(j, i, ds.size()) {
			ul z = ds[i] * ds[j];
			if (ss % z == 0)dds.push_back(z);
		}
	}
	sort(all(dds));
	dds.erase(unique(all(dds)), dds.end());
	vector<vector<ul>> ans;
	vector<ul> va;
	for (ul d : dds) {
		ul a = t - d;
		if (a <= 0 || a % 2)continue;
		a /= 2;
		if (a > 1000000000)continue;
		va.push_back(a);
	}
	for(ul a:va){
		ul d = t - 2 * a;
		ul x = ss / d;
		x += t * t;
		x -= 2 * a * t;
		if (x<=0||x % 4)continue;
		x /= 4;
		if (x > 1000000000000000000)continue;
		//cout << "?? " << a << " " << x << "\n";
		//bc=x,b+c=t-a
		ul dd = (t - a) * (t - a) - 4 * x;
		if (dd < 0)continue;
		ul bk = (sqrt(dd) + t - a) / 2;
		for (ul b = bk - 1; b <= bk + 1; b++) {
			if (x % b)continue;
			ul c = x / b;
			if (b > 100000000)continue;
			if (c > 100000000)continue;
			if (a + b + c != t)continue;
			vector<ul> v = { a,b,c };
			sort(all(v));
			if (v[0] + v[1] < v[2])continue;
			ans.push_back(v);
		}
	}
	sort(all(ans));
	ans.erase(unique(all(ans)), ans.end());
	cout << ans.size() << "\n";
	rep(i, ans.size()) {
		cout << ans[i][0] << " " << ans[i][1] << " " << ans[i][2] << "\n";
	}
}

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