#1083840 (C++23) No.2125 Inverse Sum

• 問題: No.2125 Inverse Sum
• ユーザー: anago-pie
• 提出日時: 2025-05-14 13:04:38
• 言語: C++23 (gcc 13.3.0 + boost 1.87.0)
• 結果: TLE
• 実行時間: -
• コード長: 11,230 bytes
• コンパイル時間: 3,614 ms
• コンパイル使用メモリ: 302,868 KB
• 実行使用メモリ: 7,848 KB
• 最終ジャッジ日時: 2025-05-14 13:06:29
• 合計ジャッジ時間: 7,780 ms
• ジャッジサーバーID （参考情報）: judge3 / judge5

ファイルパターン	結果
sample	AC * 3
other	AC * 2 TLE * 1 -- * 27

ソースコード

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for(int i=0; i<n; i++)
#define debug 0
#define YES cout << "Yes" << endl;
#define NO cout << "No" << endl;
using ll = long long;
using ld = long double;
const int mod = 998244353;
const int MOD = 1000000007;
const double pi = atan2(0, -1);
const int inf = 1 << 31 - 1;
const ll INF = 1LL << 63-1;
#include <time.h>
#include <chrono>
//vectorの中身を空白区切りで出力
template<typename T> 
void print1(vector<T> v) {
	for (int i = 0; i < v.size(); i++) {
		cout << v[i];
		if (i < v.size() - 1) {
			cout << " ";
		}
	}
}

//vectorの中身を改行区切りで出力
template<typename T>
void print2(vector<T> v) {
	for (auto x : v) {
		cout << x << endl;
	}
}

//二次元配列を出力
template<typename T>
void printvv(vector<vector<T>> vv) {
	for (vector<T> v : vv) {
		print1(v);
		cout << endl;
	}
}

//vectorを降順にソート
template<typename T>
void rsort(vector<T> &v) {
	sort(v.begin(), v.end());
	reverse(v.begin(), v.end());
}

//昇順priority_queueを召喚
template<typename T>
struct rpriority_queue {
	priority_queue<T, vector<T>, greater<T>> pq;

	void push(T x) {
		pq.push(x);
	}

	void pop() {
		pq.pop();
	}

	T top() {
		return pq.top();
	}

	size_t size() {
		return pq.size();
	}

	bool empty() {
		return pq.empty();
	}
};


//高速10^n計算(mod mod)
ll tenth(int n) {
	if (n == 0) {
		return 1;
	}
	else if (n % 2 == 0) {
		ll x = tenth(n / 2);
		x %= mod;
		x *= x;
		x %= mod;
		return x;
	}
	else {
		ll x = tenth(n - 1);
		x *= 10;
		x %= mod;
		return x;
	}
}


//高速a^n計算
ll power(int a, int n){
	if(n == 0){
		return 1;
	}
	else if(n % 2 == 0){
		ll x = power(a, n / 2);
		x *= x;
		return x;
	}
	else {
		ll x = power(a, n - 1);
		x *= a;
		return x;
	}
}


//n以下の素数列を生成
vector<int> prime (int n) {
	vector<bool> ch(n, false);
	vector<int> pr;
	for(int i = 2; i <= n; i++){
		if(!ch[i]){
			pr.push_back(i);
			for(int j = 1; i*j<=n; j++){
				ch[i*j]=true;
			}
		}
	}
	return pr;
}

//最大公約数(ユークリッドの互除法）
ll gcd (ll a, ll b){
	if(b>a){
		swap(a, b);
	}
	while(a%b!=0){
		ll t = a;
		a = b;
		b = t%b;
	}
	return b;
}

//最小公倍数（gcdを定義しておく）
ll lcm (ll a, ll b){
	ll g = gcd(a, b);
	ll x = (a/g)*b;
	return x;
}

//角XYZ(偏角Z→X)の角度（[0,2π)）
double angle(vector<double> X, vector<double> Y, vector<double>Z) {
	vector<double> x = { X[0] - Y[0],X[1] - Y[1] };
	vector<double> z = { Z[0] - Y[0],Z[1] - Y[1] };

	double pre, post;
	pre = atan2(x[1], x[0]);
	post = atan2(z[1], z[0]);
	if (post < 0) {
		post += pi*2;
	}
	if (pre < 0) {
		pre += pi*2;
	}
	if (pre < post) {
		pre += pi * 2;
	}
	return pre - post;
}

//mod mod下で逆元を算出する
//高速a^n計算(mod ver.)
ll mypower(ll a, ll n, ll Mod=mod) {
	if (n == 0) {
		return 1;
	}
	else if (n % 2 == 0) {
		ll x = mypower(a, n / 2,Mod);
		x *= x;
		x %= Mod;
		return x;
	}
	else {
		ll x = mypower(a, n - 1,Mod);
		x *= a;
		x %= Mod;
		return x;
	}
}
//フェルマーの小定理を利用
ll modinv(ll p, ll Mod=mod) {
	return mypower(p, Mod - 2,Mod) % Mod;
}

////素因数分解（osa_k法）（前計算O(N)、素数判定O(1)、素因数分解(O(logN)） //エラトステネスの篩の代わりとしても使える(N項のvectorを生成するため、巨大数に対しては√Nまでの素数リストを作って割る方が良い)
struct osa_k {
	//最大値までの各自然数に対し、その最小の素因数を格納するリスト
	vector<int> min_prime_list;
	int upper_limit;
	osa_k(int N) {
		//N:最大値。一つの自然数の素因数分解にしか興味が泣ければそれを入力
		vector<int> v(N + 1);
		upper_limit = N;
		rep(i, N + 1) {
			v[i] = i;
		}
		swap(min_prime_list, v);

		//k=2から見る
		for (int k = 2; k * k <= N; k++) {
			if (min_prime_list[k] == k) {
				//最小の素因数=自分ならば、素数
				//kが素数の時、t=k*kから始めてt=Nまでのkの倍数全てを確認する。未更新の自然数があれば、それの最小の素因数をkに更新する。
				//k*k未満のkの倍数に対しては、kが最小の素因数にはなり得ないので計算する必要が無い
				for (int t = k * k; t <= N; t += k) {
					if (min_prime_list[t] == t) {
						min_prime_list[t] = k;
					}
				}
			}
		}
	}

	//任意の自然数nが素数であればtrueを返す
	bool isPrime(int n) {
		if (n < 2) {
			return false;
		}
		else {
			return min_prime_list[n] == n;
		}
	}

	//任意の自然数nの素因数分解を行う。素因数はvectorで与えられる（ex:n=12 -> {2,2,3}）
	vector<int> devPrimes(int n) {
		vector<int> vec;
		int now = n;
		while (now > 1) {
			vec.push_back(min_prime_list[now]);
			now /= min_prime_list[now];
		}
		return vec;
	}
};


//最大流問題を解く構造体(Ford-Fulkerson法.O(FE))
struct maxflow {
	struct Edge {
		int to, rev;
		ll capacity, init_capacity;
		int off, on;
		Edge(int _to, int _rev, ll _capacity, int _off, int _on) :to(_to), rev(_rev), capacity(_capacity), init_capacity(_capacity), off(_off), on(_on) {};
	};
	int delay=0;
	
	vector<vector<Edge>> Graph;

	maxflow(int MAX_V, int d) {
		Graph.assign(MAX_V, {});
		delay=d;
	}

	void input(int from, int to, ll capacity, int off, int on) {
		int e_id = Graph[from].size();
		int r_id = Graph[to].size();
		Graph[from].push_back(Edge(to, r_id, capacity, off, on));
		Graph[to].push_back(Edge(from, e_id, 0, on+delay, off-delay));
	}

	Edge& rev_Edge(Edge& edge) {
		return Graph[edge.to][edge.rev];
	}

	vector<bool> visited;
	ll dfs(int now, int g, ll flow, int time) {
		visited[now] = true;
		if (now == g) {
			return flow;
		}
		else {
			ll f = 0;
			ll res_flow = flow;
			for (Edge& edge : Graph[now]) {
				if (!visited[edge.to] && edge.capacity > 0 && edge.off>=time && edge.on<=1e9) {
					ll f_delta = dfs(edge.to, g, min(res_flow, edge.capacity), edge.on+delay);	
					edge.capacity -= f_delta;
					rev_Edge(edge).capacity += f_delta;
					f += f_delta;
					res_flow -= f_delta;
					if (res_flow == 0) {
						break;
					}
				}
			}
			return f;
		}
	}

	void flowing(int s, int g, ll init_flow = INF) {
		bool cont = true;
		while (cont) {
			visited.assign(Graph.size(), false);
			ll flow = dfs(s, g, init_flow,0);
			init_flow -= flow;
			if (flow == 0) {
				cont = false;
			}
		}
	}

	ll get_flow(int g) {
		ll flow = 0;
		for (Edge& edge : Graph[g]) {
			Edge& rev_edge = rev_Edge(edge);
			ll tmp_flow = rev_edge.init_capacity - rev_edge.capacity;
			if (tmp_flow > 0) {
				flow += tmp_flow;
			}
		}
		return flow;
	}

	vector<tuple<int, int, ll>> flowing_edges() {
		vector<tuple<int, int, ll>> vec;
		rep(from, Graph.size()) {
			for (Edge& edge : Graph[from]) {
				ll flow = edge.init_capacity - edge.capacity;
				if (flow > 0) {
					vec.push_back({ from,edge.to,flow });
				}
			}
		}
		return vec;
	}
};

//Dinic法でのmax-flow。最大マッチングなど辺のキャパシティが小さい場合には高速
struct Dinic {
	struct Edge {
		int to, rev;
		ll capacity, init_capacity;
		ld cost;
		Edge(int _to, int _rev, ll _capacity,ld _cost) :to(_to), rev(_rev), capacity(_capacity),init_capacity(_capacity),cost(_cost) {};
	};

	vector<vector<Edge>> Graph;

	Edge& rev_Edge(Edge& edge) {
		return Graph[edge.to][edge.rev];
	}
	vector<int> level,itr;

	Dinic(int MAX_V) {
		Graph.assign(MAX_V, {});
	}

	void input(int _from, int _to, ll _capacity,ld _cost) {
		int e_id = Graph[_from].size(), r_id = Graph[_to].size();
		Graph[_from].push_back(Edge(_to, r_id, _capacity,_cost));
		Graph[_to].push_back(Edge(_from, e_id, 0LL,_cost));
	}

	void bfs(int s, int g, ld val) {
		level.assign(Graph.size(), -1);
		level[s] = 0;
		queue<int> q;
		q.push(s);
		while (!q.empty()) {
			int now = q.front();
			q.pop();
			if (now == g) {
				continue;
			}
			for (Edge &e : Graph[now]) {
				if (level[e.to] == -1 && e.capacity > 0 && e.cost<=val) {
					level[e.to] = level[now] + 1;
					q.push(e.to);
				}
			}
		}
	}

	ll dfs(int now, int g, ll flow, ld val) {
		if (now == g) {
			return flow;
		}
		else if (level[now] >= level[g]) {
			return 0; //gよりも深い場所に行こうとしたら終わり。flow=0を返す
		}
		else {
			ll res_flow = flow;
			ll f = 0;
			for (int &i = itr[now]; i < Graph[now].size(); i++) {
				Edge& edge = Graph[now][i];
				if (level[edge.to] == level[now] + 1 && edge.capacity > 0 && edge.cost<=val) {
					ll f_delta = dfs(edge.to, g, min(res_flow, edge.capacity), val);
					edge.capacity -= f_delta;
					rev_Edge(edge).capacity += f_delta;
					res_flow -= f_delta;
					f += f_delta;
					if (res_flow == 0) {
						break;
					}
				}
			}
			return f; //行先が無い場合はflow=0を返す
		}
	}

	void flowing(int s, int g, ll init_flow = INF, ld val=0) {
		bool cont1 = true;
		while (cont1) {
			bfs(s, g,val);
			if (level[g] == -1) {
				cont1 = false;
			}
			else {
				bool cont2 = true;
				while (cont2) {
					itr.assign(Graph.size(), 0);
					ll flow = dfs(s, g, init_flow,val);
					init_flow -= flow;
					if (flow == 0) {
						cont2 = false;
					}
				}
			}
			if(init_flow==0){
				cont1=false;
			}
		}
	}

	ll get_flow(int g) {
		ll flow = 0;
		for (Edge& edge : Graph[g]) {
			flow += max(0LL, rev_Edge(edge).init_capacity - rev_Edge(edge).capacity);
		}
		return flow;
	}

	vector<tuple<int, int, ll>> flowing_edges(){
		vector<tuple<int,int,ll>> vec;
		for (int from = 0; from < Graph.size(); from++) {
			for (Edge& edge : Graph[from]) {
				if (edge.init_capacity - edge.capacity > 0) {
					vec.push_back({ from,edge.to,edge.init_capacity - edge.capacity });
				}
			}
		}
		return vec;
	}

	void reset() {
		for (int from = 0; from < Graph.size(); from++) {
			for (Edge& edge : Graph[from]) {
				edge.capacity = edge.init_capacity;
			}
		}
	}
};

struct SegTree{
	vector<int> tree;
	int n=1;
	SegTree(int N){
		while(n<N){
			n*=2;
		}
		tree.assign(n*2,0);
	}

	void update(int now){
		tree[now]=tree[now*2+1]+tree[now*2+2];
		if(now>0){
			update((now-1)/2);
		}
	}

	void add(int i, int d){
		tree[n-1+i]+=d;
		update((n-2+i)/2);
	}

	int sum(int l, int r, int b, int u, int now){
		if(r<=b || l>=u){
			return 0;
		}
		else if(l<=b && r>=u){
			return tree[now];
		}
		else{
			return sum(l,r,b,(b+u)/2,now*2+1)+sum(l,r,(b+u)/2,u,now*2+2);
		}
	}

	int query(int L, int R){
		return sum(L,R+1,0,n,0);
	}
};

int main(){
	ll P,Q;
	cin>>P>>Q;
	ll g=gcd(P,Q);
	ll p=P/g, q=Q/g;
	if(p>q*2){
		cout<<0<<endl;
	}
	else if(p==q*2){
		cout<<1<<endl<<"1 1"<<endl;
	}
	else{
		set<vector<ll>> s;
		ll k=1;
		{
			ll l=0, r=1e9+5;
			while(r>l+1){
				ll mid=(l+r)/2;
				if(sqrt(ld(mid*q))*2<=mid*p){
					r=mid;
				}
				else{
					l=mid;
				}
			}
			k=r;
		}
		
		ll x=floor(sqrt(k*q));
		while(x>=1){
			ld py=k*p-x, qy=ld(k*q)/ld(x);
			if(qy<py){
				ll l=k,r=1e9+5;
				while(r>l+1){
					ll mid=(l+r)/2;
					if(ld(mid*q)/ld(x) < mid*p-x){
						l=mid;
					}
					else{
						r=mid;
					}
				}
				k=r;
				py=k*p-x, qy=ld(k*q)/ld(x);
			}
			if(py==qy){
				s.insert({x,ll(py)});
				s.insert({ll(py),x});
			}
			x--;
		}

		cout<<s.size()<<endl;
		for(vector<ll> v:s){
			cout<<v[0]<<" "<<v[1]<<endl;
		}
	}
}