#938801 (C++17) No.2589 Prepare Integers

提出ソース
結果

問題	No.2589 Prepare Integers
コンテスト
ユーザー	heno239
提出日時	2023-12-17 04:01:40
言語	C++17 (gcc 13.3.0 + boost 1.87.0)
結果	WA
実行時間	-
コード長	10,487 bytes
コンパイル時間	2,940 ms
コンパイル使用メモリ	182,788 KB
最終ジャッジ日時	2025-02-18 11:53:59
ジャッジサーバーID （参考情報）	judge3 / judge5
このコードへのチャレンジ
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ファイルパターン	結果
sample	AC * 4
other	AC * 11 WA * 13
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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;
//ll mod = 1;
constexpr ll mod = 998244353;
//constexpr ll mod = 1000000009;
const int mod17 = 1000000007;
const ll INF = (ll)mod17 * mod17;
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;

using ld = double;
typedef pair<ld, ld> LDP;
const ld eps = 1e-10;
const ld pi = acosl(-1.0);

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>
vector<T> vmerge(vector<T>& a, vector<T>& b) {
	vector<T> res;
	int ida = 0, idb = 0;
	while (ida < a.size() || idb < b.size()) {
		if (idb == b.size()) {
			res.push_back(a[ida]); ida++;
		}
		else if (ida == a.size()) {
			res.push_back(b[idb]); idb++;
		}
		else {
			if (a[ida] < b[idb]) {
				res.push_back(a[ida]); ida++;
			}
			else {
				res.push_back(b[idb]); idb++;
			}
		}
	}
	return res;
}
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;
}
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 };

//------------------------------------

//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;
}

void solve() {
	int b, q; cin >> b >> q;

	int sz = 0;
	{
		ll t = 1;
		while (t < mod17) {
			t *= b; sz++;
		}
	}
	ll sup = 1;
	{
		ll t = 1;
		rep(i, sz) {
			sup += t * (b - 1);
			t *= b;
		}
		sup++;
	}
	vector<vector<ll>> bs;
	vector<vector<ll>> lateradds;
	auto addlater = [&](vector<ll> v) {
		lateradds.push_back(v);
		rep(j, v.size()) {
			if (v[j] != 0) {
				ll g = gcd(v[j], b);
				vector<ll> nv = v;
				rep(i, nv.size()) {
					nv[i] *= b / g;
					nv[i] %= b;
				}
				lateradds.push_back(nv);
			}
		}
	};
	auto add_ = [&](vector<ll> v) {
		int id = 0;
		int idv = 0;
		vector<vector<ll>> rads;
		rep(i, bs.size()) {
			while (bs[i][id] == 0)id++;
			while (idv < v.size() && v[idv] == 0)idv++;
			if (idv == v.size())return;
			if (idv < id) {
				//modify v
				ll g = gcd(b, v[idv]);
				ll x = mod_inverse(v[idv] / g, b / g);
				rep(j, v.size()) {
					(v[j] *= x) %= b;
				}
				assert(v[idv] == g);
				bs.insert(bs.begin() + i, v);
				addlater(v);
				return;
			}
			else if (idv == id) {
				{
					//modify v
					ll g = gcd(b, v[idv]);
					ll x = mod_inverse(v[idv] / g, b / g);
					rep(j, v.size()) {
						(v[j] *= x) %= b;
					}
				}
				ll g = gcd(bs[i][id], v[idv]);
				assert(b % g == 0);
				if (g != bs[i][id]) {
					ll x, y;
					extgcd(bs[i][id], v[idv], x, y);
					x %= b;
					y %= b;
					//cout << "?? " << x << " " << y << "\n";
					vector<ll> nv(sz);
					rep(j, nv.size()) {
						nv[j] = bs[i][j] * x + v[j] * y;
						nv[j] %= b; if (nv[j] < 0)nv[j] += b;
					}
					assert(nv[id] == g);
					swap(bs[i], nv);
					addlater(nv);
					addlater(bs[i]);
					
				}
				assert(bs[i][id] == g);
				ll coef = v[idv] / g;
				Rep(j, idv, sz) {
					v[j] -= coef * bs[i][j];
					v[j] %= b; if (v[j] < 0)v[j] += b;
				}
				addlater(v); return;
			}
		}
		while (idv < v.size() && v[idv] == 0)idv++;
		if (idv != v.size()) {
			//modify v
			ll g = gcd(b, v[idv]);
			ll x = mod_inverse(v[idv] / g, b / g);
			rep(j, v.size()) {
				(v[j] *= x) %= b;
			}
			assert(v[idv] == g);
			bs.push_back(v);
			addlater(v);
		}
	};
	auto add = [&](vector<ll> v) {
		addlater(v);
		while (lateradds.size()) {
			auto v = lateradds.back();
			lateradds.pop_back();
			add_(v);
		}
	};
	//v未満の個数
	auto query_ = [&](vector<ll> v)->ll {
		ll res = 0;
		vector<int> ids(bs.size());
		vector<ll> gs(bs.size());
		vector<ll> rgs(bs.size() + 1, 1);
		{
			int id = 0;
			rep(i, bs.size()) {
				while (bs[i][id] == 0)id++;
				ids[i] = id;
				assert(b % bs[i][id] == 0);
				gs[i] = b / bs[i][id];
			}
			per(i, (int)bs.size()) {
				rgs[i] = rgs[i + 1] * gs[i];
			}
		}
		vector<ll> adl(sz);
		rep(i, ids.size()) {
			int le = 0;
			if (i > 0)le = ids[i - 1] + 1;
			int ri = ids[i];
			Rep(j, le,ri) {
				if (adl[j] < v[j]) {
					res += rgs[i]; return res;
				}
				else if (adl[j] > v[j]) {
					return res;
				}
			}
			int id = ids[i];
			ll d = adl[id] / bs[i][id];
			Rep(j, id, sz) {
				adl[j] -= d * bs[i][j];
				adl[j] %= b;
				if (adl[j] < 0)adl[j] += b;
			}
			assert(adl[id] < bs[i][id]);
			if (adl[id] > v[id])return res;
			d = (v[id] - adl[id]) / bs[i][id];
			res += rgs[i + 1] * d;
			if ((v[id] - adl[id]) % bs[i][id]) {
				res += rgs[i + 1]; return res;
			}
			Rep(j, id, sz) {
				adl[j] += d * bs[i][j];
				adl[j] %= b;
			}
			assert(adl[id] == v[id]);
			rep(j, id + 1)assert(adl[j] == v[j]);
		}
		int le = 0;
		if (ids.size())le = ids.back();
		Rep(j, le + 1, sz) {
			if (adl[j] < v[j]) {
				res += 1; return res;
			}
			else if (adl[j] > v[j]) {
				return res;
			}
		}
		return res;
	};
	auto trans = [&](ll x) {
		vector<ll> res(sz);
		per(i, sz) {
			res[i] = x % b; x /= b;
		}
		return res;
	};
	auto query = [&](ll x) {
		if (x == sup) {
			int id = 0;
			ll res = 1;
			rep(i, bs.size()) {
				while (bs[i][id] == 0)id++;
				assert(b % bs[i][id] == 0);
				res *= b / bs[i][id];
			}
			return res;
		}
		ll res = query_(trans(x));
		//cout <<"val "<< x << " " << res << "\n";
		return res;
	};
	
	//cout << "??? " << sup << "\n";
	rep(i, q) {
		int t; ll x; cin >> t >> x;
		if (t == 1) {
			add(trans(x));
		}
		else if (t == 2) {
			x--;
			ll le = -1, ri = sup;
			while (ri - le > 1) {
				ll mid = (le + ri) / 2;
				if (query(mid) > x)ri = mid;
				else le = mid;
			}
			if (ri == sup)le = -1;
			cout << le << "\n";
		}
		else {
			chmin(x, sup - 1);
			cout << query(x+1) << "\n";
		}
		/*cout << "hello " << i << "\n";
		rep(j, bs.size())coutarray(bs[j]);
		cout << "fin\n";*/
		/*rep(j, 10) {
			cout << "!? " << j<<" "<<query(j) << "\n";
		}*/
	}
}



signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed<<setprecision(10);
	//init_f();
	//init();
	//while(true)
	//expr();
	//int t; cin >> t; rep(i, t)
	solve();
	return 0;
}
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結果

ソースコード
