結果

問題 No.1309 テスト
ユーザー heno239
提出日時 2020-12-06 22:23:20
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 369 ms / 4,000 ms
コード長 8,518 bytes
コンパイル時間 2,495 ms
コンパイル使用メモリ 148,432 KB
最終ジャッジ日時 2025-01-16 18:43:04
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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 * 2
other AC * 85
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("Ofast")
#pragma GCC target ("sse4")

#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 double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-12;
const ld pi = acosl(-1.0);

ll mod_pow(ll x, ll n, ll m = mod) {
	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)); }

const int max_n = 1 << 17;
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];
}

ll calc2(ll x) {
	return x * (x + 1) / 2;
}

P v[100];
int cur;


int divk1[1001][1001];
int rrrk1[1001][1001];
void init() {
	for (int i = 0; i <= 1000; i++) {
		for (int k = 2; k <= 1000; k++) {
			divk1[k][i] = i / (k - 1);
			rrrk1[k][i] = i % (k - 1);
		}
	}
}
ll memo[4][1005];
void solve() {
	int n; ll p, x, y; cin >> n >> p >> x >> y;
	if (n == 1) {
		if (x == y) {
			cout << x << "\n";
		}
		else {
			cout << -1 << "\n";
		}
		return;
	}
	ll ans = -1;
	//0
	rep(i, 1005)memo[0][i] = calc2(i);
	//x-i
	rep(i, 1005)memo[1][i] = calc2(x - i);
	//x+i
	rep(i, 1005)memo[2][i] = calc2(x + i);
	//p-i
	rep(i, 1005)memo[3][i] = calc2(p - i);
	auto cs = [&](int restl, int restr, int cl, int cr, int k, ll s, ll ad)->ll {
		//if (k == 1)return -INF;
		int xl = restl - cl * k;
		int xr = restr - cr * k;
		ll sum = 0;
		int dl = divk1[k][xl];
		int dr = divk1[k][xr];
		int rl = rrrk1[k][xl];
		int rr = rrrk1[k][xr];
		int nl = dl + (rl > 0);
		int nr = dr + (rr > 0);
		if (nl + cl > x)return -1;
		if (nr + cr > p - x)return -2;
		//[0,x),(x,p]
		ll mi = memo[0][cl - 1] + memo[2][cr] - memo[2][0];
		if (mi > s)return -2;
		ll ma = memo[1][1 + nl] - memo[1][1 + nl + cl];
		ma += memo[3][nr] - memo[3][nr + cr];
		ll b = 0;
		b += (k - 1) * (memo[1][1] - memo[1][1 + dl]);
		b += (x - 1 - dl) * rl;
		b += (memo[3][0] - memo[3][dr]) * (k - 1);
		b += (p - dr) * rr;
		if (s <= ma) {
			return b + ad;
		}
		else {
			ll sup = memo[1][1] - memo[1][1 + cl];
			sup += memo[3][0] - memo[3][cr];
			//cout << "?? " << sup << "\n";
			if (sup < s)return -1;
		    int dif = s - ma;
			//cost,number
			cur = 0;
			if (rl > 0) {
				v[cur] = { rl,cl }; cur++;
			}
			if (rr > 0) {
				v[cur] = { rr,cr }; cur++;
				if (cur == 2 && v[0].first > v[1].first)swap(v[0], v[1]);
			}
			if (cl > 0 && dl > 0) {
				v[cur] = { k - 1,cl * dl }; cur++;
			}
			if (cr > 0 && dr > 0) {
				v[cur] = { k - 1,cr * dr }; cur++;
			}
			rep(i, cur) {
				ll z = min(v[i].second, dif);
				dif -= z;
				b -= z * v[i].first;
			}
			return b + ad;
		}
		return -INF;
	};
	auto cs2 = [&](int lsup,int restr, int cl, int cr, int k, ll s, ll ad)->ll {
		//if (k == 1)return -INF;
		int xl = n / 2-cl*k;
		lsup = min(lsup, xl);
		int xr = restr - cr * k;
		ll sum = 0;
		int nl = 0;

		int dl = divk1[k][xl - lsup];
		nl += dl;
		int rl = rrrk1[k][xl - lsup];
		if (rl > 0) {
			nl++;
		}
		int dr = divk1[k][xr];
		int rr = rrrk1[k][xr];
		int nr = dr + (rr > 0);
		if (nl + cl > x)return -1;
		if (nr + cr > p - x)return -2;
		//[0,x),(x,p]
		ll mi = memo[0][cl - 1] + memo[2][cr] - memo[2][0];
		if (mi > s)return -2;
		ll ma = memo[1][1 + nl] - memo[1][1 + nl + cl];
		ma += memo[3][nr] - memo[3][nr + cr];
		ll b = 0;
		b += x * lsup;
		b += (k - 1) * (memo[1][1] - memo[1][1 + dl]);
		b += (x - 1 - dl) * rl;
		b += (memo[3][0] - memo[3][dr]) * (k - 1);
		b += (p - dr) * rr;
		if (s <= ma) {
			return b + ad;
		}
		else {
			ll sup = memo[1][1] - memo[1][1 + cl];
			sup += memo[3][0] - memo[3][cr];
			//cout << "?? " << sup << "\n";
			if (sup < s)return -1;
			int dif = s - ma;
			//cost,number
			cur = 0;
			if (rl > 0) {
				v[cur] = { rl,cl }; cur++;
			}
			if (rr > 0) {
				v[cur] = { rr,cr }; cur++;
				if (cur==2&&v[0].first > v[1].first)swap(v[0], v[1]);
			}
			if (cl > 0 && dl > 0) {
				v[cur] = { k - 1,cl * dl }; cur++;
			}
			if (cr > 0 && dr > 0) {
				v[cur] = { k - 1,cr * dr }; cur++;
			}
			rep(i, cur) {
				ll z = min(v[i].second, dif);
				dif -= z;
				b -= z * v[i].first;
			}
			return b + ad;
		}
		return -INF;
	};

	if (x == p) {
		if (y == p) {
			cout << n * p << "\n";
		}
		else {
			cout << -1 << "\n";
		}
	}
	else if (x == 0) {
		if (y == 0) {
			cout << (n / 2) * p << "\n";
		}
		else {
			cout << -1 << "\n";
		}
	}
	else {
		int tmp = 0;
		//include x
		for (int cr = 0; cr <= n / 2; cr++) {
			for (int k = cr + 1; k <= n; k++) {
				if (k == 1)continue;
				int cl = k - 1 - cr;
				if (cl > n / 2)continue;
				if (cl + cr + 1 > n / 2) {
					if (x == y) {
						ll val = cs(n / 2 - cl, n / 2 - cr, 0, 0, cl + cr + 1, 0, (cl + cr + 1) * x);
						ans = max(ans, val);
					}
					continue;
				}
				int sl = (n / 2 - cl) / k;
				int sr = (n / 2 - cr) / k;
				for (int le = 0; le <= sl; le++) {
					for (int ri = 0; ri <= sr; ri++) {
						tmp++;
						int num = le + ri;
						if (k == cl + cr + 1)num++;
						if (num == 0)continue;

						ll sum = num * y;
						if (k == cl + cr + 1)sum -= x;
						ll z = num * y * k;
						if (k != cl + cr + 1)z += (cl + cr + 1) * x;
						ll val = cs(n / 2 - cl, n / 2 - cr, le, ri, k, sum, z);
						ans = max(ans, val);
						//cout << cl << " " << cr << " " << k << " " << le << " " << ri << " " << val << "\n";
					}
				}
			}
		}
		//don't include x
		for (int cr = 0; cr <= n / 2; cr++) {
			for (int k = cr + 2; k <= n/2; k++) {
				int sl = (n / 2) / k;
				int sr = (n / 2 - cr) / k;
				for (int le = 0; le <= sl; le++) {
					for (int ri = 0; ri <= sr; ri++) {
						int num = le + ri;
						if (num == 0)continue;

						ll sum = num * y;
						ll z = num * y * k;
						z += (cr + 1) * x;
						ll val = cs2(k-(cr+2), n / 2 - cr, le, ri, k, sum, z);
						ans = max(ans, val);
						//cout << cr << " " << k << " " << sl << " " << sr << " " << val << "\n";
					}
				}
			}
		}

		//cout << tmp << "\n";
		if (x >= n / 2 && p - x >= n / 2) {
			ll d = n / 2;
			ll l1 = calc2(d - 1);
			ll r1 = calc2(x - 1) - calc2(x - 1 - d);
			ll l2 = calc2(x + d) - calc2(x);
			ll r2 = calc2(p) - calc2(p - d);
			ll sl = l1 + l2 + x;
			ll sr = r1 + r2 + x;
			if (sl <= n * y && n * y <= sr) {
				ans = max(ans, n * y);
			}
		}
		if (ans<0)ans = -1;
		cout << ans << "\n";
	}
}

signed main() {

	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(15);
	//init_f();
	init();
	//expr();
	//int t; cin >> t; rep(i, t)
	int t = 10; rep(i, t)
		solve();
	return 0;
}
0