// clang-format off #ifdef _LOCAL #include #else #include #define cerr if (false) cerr #define debug_bar #define debug(...) #define debug2(vv) #define debug3(vvv) #endif using namespace std; using ll = long long; using ld = long double; using str = string; using P = pair; using VP = vector

; using VVP = vector; using VC = vector; using VS = vector; using VVS = vector; using VI = vector; using VVI = vector; using VVVI = vector; using VLL = vector; using VVLL = vector; using VVVLL = vector; using VB = vector; using VVB = vector; using VVVB = vector; using VD = vector; using VVD = vector; using VVVD = vector; #define FOR(i,l,r) for (ll i = (l); i < (r); ++i) #define RFOR(i,l,r) for (ll i = (r)-1; (l) <= i; --i) #define REP(i,n) FOR(i,0,n) #define RREP(i,n) RFOR(i,0,n) #define FORE(e,c) for (auto&& e : c) #define ALL(c) (c).begin(), (c).end() #define SORT(c) sort(ALL(c)) #define RSORT(c) sort((c).rbegin(), (c).rend()) #define MIN(c) *min_element(ALL(c)) #define MAX(c) *max_element(ALL(c)) #define COUNT(c,v) count(ALL(c),(v)) #define len(c) ((ll)(c).size()) #define BIT(b,i) (((b)>>(i)) & 1) #define PCNT(b) ((ll)__builtin_popcountll(b)) #define LB(c,v) distance((c).begin(), lower_bound(ALL(c), (v))) #define UB(c,v) distance((c).begin(), upper_bound(ALL(c), (v))) #define UQ(c) do { SORT(c); (c).erase(unique(ALL(c)), (c).end()); (c).shrink_to_fit(); } while (0) #define END(...) do { print(__VA_ARGS__); exit(0); } while (0) constexpr ld EPS = 1e-10; constexpr ld PI = acosl(-1.0); constexpr int inf = (1 << 30) - (1 << 15); // 1,073,709,056 constexpr ll INF = (1LL << 62) - (1LL << 31); // 4,611,686,016,279,904,256 template void input(T&... a) { (cin >> ... >> a); } void print() { cout << '\n'; } template void print(const T& a) { cout << a << '\n'; } template void print(const pair& a) { cout << a.first << " " << a.second << '\n'; } template void print(const T& a, const Ts&... b) { cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; } template void cout_line(const vector& ans, int l, int r) { for (int i = l; i < r; i++) { if (i != l) { cout << ' '; } cout << ans[i]; } cout << '\n'; } template void print(const vector& a) { cout_line(a, 0, a.size()); } template bool chmin(S& a, const T b) { if (b < a) { a = b; return 1; } return 0; } template bool chmax(S& a, const T b) { if (a < b) { a = b; return 1; } return 0; } template T SUM(const vector& A) { return accumulate(ALL(A), T(0)); } template vector cumsum(const vector& A, bool offset = false) { int N = A.size(); vector S(N+1, 0); for (int i = 0; i < N; i++) { S[i+1] = S[i] + A[i]; } if (not offset) { S.erase(S.begin()); } return S; } template string to_binary(T x, int B = 0) { string s; while (x) { s += ('0' + (x & 1)); x >>= 1; } while ((int)s.size() < B) { s += '0'; } reverse(s.begin(), s.end()); return s; } template ll binary_search(const F& is_ok, ll ok, ll ng) { while (abs(ok - ng) > 1) { ll m = (ok + ng) / 2; (is_ok(m) ? ok : ng) = m; } return ok; } template double binary_search_real(const F& is_ok, double ok, double ng, int iter = 90) { for (int i = 0; i < iter; i++) { double m = (ok + ng) / 2; (is_ok(m) ? ok : ng) = m; } return ok; } template using PQ_max = priority_queue; template using PQ_min = priority_queue, greater>; template T pick(stack& s) { assert(not s.empty()); T x = s.top(); s.pop(); return x; } template T pick(queue& q) { assert(not q.empty()); T x = q.front(); q.pop(); return x; } template T pick_front(deque& dq) { assert(not dq.empty()); T x = dq.front(); dq.pop_front(); return x; } template T pick_back(deque& dq) { assert(not dq.empty()); T x = dq.back(); dq.pop_back(); return x; } template T pick(PQ_min& pq) { assert(not pq.empty()); T x = pq.top(); pq.pop(); return x; } template T pick(PQ_max& pq) { assert(not pq.empty()); T x = pq.top(); pq.pop(); return x; } template T pick(vector& v) { assert(not v.empty()); T x = v.back(); v.pop_back(); return x; } int to_int(const char c) { if (islower(c)) { return (c - 'a'); } if (isupper(c)) { return (c - 'A'); } if (isdigit(c)) { return (c - '0'); } assert(false); } char to_a(const int i) { assert(0 <= i && i < 26); return ('a' + i); } char to_A(const int i) { assert(0 <= i && i < 26); return ('A' + i); } char to_d(const int i) { assert(0 <= i && i <= 9); return ('0' + i); } ll min(int a, ll b) { return min((ll)a, b); } ll min(ll a, int b) { return min(a, (ll)b); } ll max(int a, ll b) { return max((ll)a, b); } ll max(ll a, int b) { return max(a, (ll)b); } ll mod(ll x, ll m) { assert(m > 0); return (x % m + m) % m; } ll ceil(ll a, ll b) { if (b < 0) { return ceil(-a, -b); } assert(b > 0); return (a < 0 ? a / b : (a + b - 1) / b); } ll floor(ll a, ll b) { if (b < 0) { return floor(-a, -b); } assert(b > 0); return (a > 0 ? a / b : (a - b + 1) / b); } ll powint(ll x, ll n) { assert(n >= 0); if (n == 0) { return 1; }; ll res = powint(x, n>>1); res *= res; if (n & 1) { res *= x; } return res; } pair divmod(ll a, ll b) { assert(b != 0); ll q = floor(a, b); return make_pair(q, a - q * b); } ll bitlen(ll b) { if (b <= 0) { return 0; } return (64LL - __builtin_clzll(b)); } ll digitlen(ll n) { assert(n >= 0); if (n == 0) { return 1; } ll sum = 0; while (n > 0) { sum++; n /= 10; } return sum; } ll msb(ll b) { return (b <= 0 ? -1 : (63 - __builtin_clzll(b))); } ll lsb(ll b) { return (b <= 0 ? -1 : __builtin_ctzll(b)); } // -------------------------------------------------------- // 座標圧縮 template struct compress { public: compress() {} compress(const vector& A) : xs(A) {} compress(const vector& A, const vector& B) { xs.reserve(A.size() + B.size()); for (const auto& a : A) { xs.push_back(a); } for (const auto& b : B) { xs.push_back(b); } } // 値 v を追加する // - amortized O(1) void add(T v) { assert(not is_built); xs.push_back(v); } // 配列 A の値を全て追加する // - O(|A|) void add(const vector& A) { assert(not is_built); xs.reserve(xs.size() + A.size()); for (const auto& a : A) { xs.push_back(a); } } // 座標圧縮して種類数を返す // - O(N log N) int build() { assert(not is_built); sort(xs.begin(), xs.end()); xs.erase(unique(xs.begin(), xs.end()), xs.end()); is_built = true; return xs.size(); } // 座標圧縮前で i 番目に大きい値を返す (0-indexed) // - O(1) T operator[] (int i) const noexcept { assert(is_built); assert(0 <= i && i < (int)xs.size()); return xs[i]; } // 値 v に対応する座標圧縮後の値(番号)を返す // 値 v が元の配列に存在することを想定 // - O(log N) int operator() (T v) const noexcept { assert(is_built); auto it = lower_bound(xs.begin(), xs.end(), v); assert(it != xs.end() && *it == v); return distance(xs.begin(), it); } // 座標圧縮後の値の種類数を返す // - O(1) int size() const noexcept { assert(is_built); return xs.size(); } private: bool is_built = false; vector xs; }; // References: // // // // // Convex Hull Trick (Li-Chao Segment Tree) // - 座標圧縮をしておく必要あり (x_1 < x_2 < ... < x_n) // - 最大値取得をしたい場合はマイナスを付けて直線追加して結果にもマイナスを付ける // - (a, b) -> (-a, -b) // - query() -> query() * (-1) // - 下記を想定(必要に応じて調整) // - max(x) < INF_x // - max(y) < INF_y struct LiChaoSegtree { public: LiChaoSegtree(int n, const vector& ps, ll inf_x = -1, ll inf_y = -1) { N = 1; while (N < n) { N <<= 1; } xs.resize(2*N); p.resize(2*N); q.resize(2*N); used.resize(2*N, false); if (inf_x == -1) { INF_x = *max_element(ps.begin(), ps.end()) + 1; } if (inf_y == -1) { INF_y = INF; } for (int i = 0; i < n; i++) { xs[i] = ps[i]; } for (int i = n; i < 2*N; i++) { xs[i] = INF_x; } } // 直線 (a,b) の追加 // - O(log N) void add_line(ll a, ll b) { _add_line(a, b, 0, 0, N); } // 区間 [x_l, x_r) に対する線分 (a,b) の追加 // - O(log N) void add_segment_line(ll a, ll b, int l, int r) { int L = l + N, R = r + N; int sz = 1; while (L < R) { if (L & 1) { _add_line(a, b, L-1, l, l+sz); L++; l += sz; } if (R & 1) { R--; r -= sz; _add_line(a, b, R-1, r, r+sz); } L >>= 1; R >>= 1; sz <<= 1; } } // i 番目の座標に対する最小値を返す // - O(log N) ll query(int i) const { ll x = xs[i]; int k = i + (N - 1); ll res = (used[k] ? p[k]*x + q[k] : INF_y); while (k > 0) { k = (k - 1) / 2; if (used[k]) { chmin(res, p[k]*x + q[k]); } } return res; } private: int N; // 座標の数 ll INF_x; // 葉ノード以外のダミー座標 ll INF_y; // 最小値クエリの初期値 vector xs, p, q; // 座標・傾き・接線 vector used; // ノードが一度も使用されていなければ false // 区間 [l,r) に対する直線 (a,b) の追加処理 : O(log N) void _add_line(ll a, ll b, int k, int l, int r) { while (l < r) { if(not used[k]) { used[k] = true; p[k] = a; q[k] = b; return; } int m = (l + r) / 2; ll lx = xs[l], mx = xs[m], rx = xs[r-1]; ll pk = p[k], qk = q[k]; bool left = (a*lx + b < pk*lx + qk); bool mid = (a*mx + b < pk*mx + qk); bool right = (a*rx + b < pk*rx + qk); if (left && right) { // 直線 (a,b) が全勝 p[k] = a; q[k] = b; return; } else if (not left && not right) { // 直線 (p,q) が全勝 return; } else if (mid) { // swap することで探索区間を片側だけに減らすテク swap(p[k], a); swap(q[k], b); } else if (left != mid) { // [l,m) で直線 (a,b) が勝つ部分あり k = 2*k + 1; r = m; } else { // [m,r) で直線 (a,b) が勝つ部分あり k = 2*k + 2; l = m; } } } }; // clang-format on int main() { ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(15); ll a; input(a); ll Q; input(Q); VLL q(Q), s(Q), t(Q); REP (i, Q) { input(q[i]); if (q[i] == 1) { input(s[i], t[i]); } else { input(t[i]); } } compress z(t); ll M = z.build(); VLL T(M); REP (m, M) { T[m] = z[m]; } LiChaoSegtree cht(M, T); REP (i, Q) { if (q[i] == 1) { ll A = a * (s[i] + t[i]); ll B = -a * s[i] * t[i]; cht.add_line(-A, -B); } else { ll ans = -cht.query(z(t[i])) + (-a * t[i] * t[i]); chmax(ans, 0); print(ans); } } return 0; }