#pragma GCC optimize("Ofast") #pragma GCC target ("sse4") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include 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 pairP; #define stop char nyaa;cin>>nyaa; #define rep(i,n) for(int i=0;i=0;i--) #define Rep(i,sta,n) for(int i=sta;i=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) #define all(v) (v).begin(),(v).end() typedef pair LP; typedef double ld; typedef pair 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; 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 cnl = 0; int sl = x; if (lsup > 0) { sl++; cnl++; } int dl = divk1[k][xl - lsup]; nl += dl; cnl += dl; int rl = rrrk1[k][xl - lsup]; if (rl > 0) { nl++; cnl++; } int dr = divk1[k][xr]; int rr = rrrk1[k][xr]; int nr = dr + (rr > 0); if (cnl + cl > sl)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 (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 + 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 == -INF)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; }