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#define PROBLEM "https://judge.yosupo.jp/problem/point_set_range_composite" #include <bits/stdc++.h> using namespace std; #include "../SegTree.h" #include "../../Math/modint.h" #include "../../buffered_reader.h" using modular = ModInt<998244353>; struct Func { modular a, b; }; Func op(Func l, Func r) { return Func{ l.a * r.a, r.a * l.b + r.b }; } Func e() { return Func{1, 0}; } int32_t main() { ios::sync_with_stdio(0); cin.tie(0); int n = IO::get<int>(); int q = IO::get<int>(); vector<Func> funcs(n); for (auto& f : funcs) { int a = IO::get<int>(); int b = IO::get<int>(); f = {a, b}; } SegTree<Func, op, e> seg_tree(funcs); while (q--) { int typ = IO::get<int>(); if (typ == 0) { int pos = IO::get<int>(); int a = IO::get<int>(); int b = IO::get<int>(); seg_tree.set(pos, {a, b}); } else { int l = IO::get<int>(); int r = IO::get<int>(); auto f = seg_tree.prod(l, r); modular x(IO::get<int>()); cout << f.a * x + f.b << '\n'; } } return 0; }
#line 1 "DataStructure/test/segment_tree_pointsetrangecomposite.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/point_set_range_composite" #include <bits/stdc++.h> using namespace std; #line 1 "DataStructure/SegTree.h" // SegTree, copied from AtCoder library {{{ // AtCoder doc: https://atcoder.github.io/ac-library/master/document_en/segtree.html // // Notes: // - Index of elements from 0 -> n-1 // - Range queries are [l, r-1] // // Tested: // - (binary search) https://atcoder.jp/contests/practice2/tasks/practice2_j // - https://oj.vnoi.info/problem/gss // - https://oj.vnoi.info/problem/nklineup // - (max_right & min_left for delete position queries) https://oj.vnoi.info/problem/segtree_itstr // - https://judge.yosupo.jp/problem/point_add_range_sum // - https://judge.yosupo.jp/problem/point_set_range_composite int ceil_pow2(int n) { int x = 0; while ((1U << x) < (unsigned int)(n)) x++; return x; } template< class T, // data type for nodes T (*op) (T, T), // operator to combine 2 nodes T (*e)() // identity element > struct SegTree { SegTree() : SegTree(0) {} explicit SegTree(int n) : SegTree(vector<T> (n, e())) {} explicit SegTree(const vector<T>& v) : _n((int) v.size()) { log = ceil_pow2(_n); size = 1<<log; d = vector<T> (2*size, e()); for (int i = 0; i < _n; i++) d[size+i] = v[i]; for (int i = size - 1; i >= 1; i--) { update(i); } } // 0 <= p < n void set(int p, T x) { assert(0 <= p && p < _n); p += size; d[p] = x; for (int i = 1; i <= log; i++) update(p >> i); } // 0 <= p < n T get(int p) const { assert(0 <= p && p < _n); return d[p + size]; } // Get product in range [l, r-1] // 0 <= l <= r <= n // For empty segment (l == r) -> return e() T prod(int l, int r) const { assert(0 <= l && l <= r && r <= _n); T sml = e(), smr = e(); l += size; r += size; while (l < r) { if (l & 1) sml = op(sml, d[l++]); if (r & 1) smr = op(d[--r], smr); l >>= 1; r >>= 1; } return op(sml, smr); } T all_prod() const { return d[1]; } // Binary search on SegTree to find largest r: // f(op(a[l] .. a[r-1])) = true (assuming empty array is always true) // f(op(a[l] .. a[r])) = false (assuming op(..., a[n]), which is out of bound, is always false) template <bool (*f)(T)> int max_right(int l) const { return max_right(l, [](T x) { return f(x); }); } template <class F> int max_right(int l, F f) const { assert(0 <= l && l <= _n); assert(f(e())); if (l == _n) return _n; l += size; T sm = e(); do { while (l % 2 == 0) l >>= 1; if (!f(op(sm, d[l]))) { while (l < size) { l = (2 * l); if (f(op(sm, d[l]))) { sm = op(sm, d[l]); l++; } } return l - size; } sm = op(sm, d[l]); l++; } while ((l & -l) != l); return _n; } // Binary search on SegTree to find smallest l: // f(op(a[l] .. a[r-1])) = true (assuming empty array is always true) // f(op(a[l-1] .. a[r-1])) = false (assuming op(a[-1], ..), which is out of bound, is always false) template <bool (*f)(T)> int min_left(int r) const { return min_left(r, [](T x) { return f(x); }); } template <class F> int min_left(int r, F f) const { assert(0 <= r && r <= _n); assert(f(e())); if (r == 0) return 0; r += size; T sm = e(); do { r--; while (r > 1 && (r % 2)) r >>= 1; if (!f(op(d[r], sm))) { while (r < size) { r = (2 * r + 1); if (f(op(d[r], sm))) { sm = op(d[r], sm); r--; } } return r + 1 - size; } sm = op(d[r], sm); } while ((r & -r) != r); return 0; } private: int _n, size, log; vector<T> d; void update(int k) { d[k] = op(d[2*k], d[2*k+1]); } }; // }}} // SegTree examples {{{ // Examples: Commonly used SegTree ops: max / min / sum struct MaxSegTreeOp { static int op(int x, int y) { return max(x, y); } static int e() { return INT_MIN; } }; struct MinSegTreeOp { static int op(int x, int y) { return min(x, y); } static int e() { return INT_MAX; } }; struct SumSegTreeOp { static long long op(long long x, long long y) { return x + y; } static long long e() { return 0; } }; // using STMax = SegTree<int, MaxSegTreeOp::op, MaxSegTreeOp::e>; // using STMin = SegTree<int, MinSegTreeOp::op, MinSegTreeOp::e>; // using STSum = SegTree<int, SumSegTreeOp::op, SumSegTreeOp::e>; // }}} #line 1 "Math/modint.h" // ModInt {{{ template<int MD> struct ModInt { using ll = long long; int x; constexpr ModInt() : x(0) {} constexpr ModInt(ll v) { _set(v % MD + MD); } constexpr static int mod() { return MD; } constexpr explicit operator bool() const { return x != 0; } constexpr ModInt operator + (const ModInt& a) const { return ModInt()._set((ll) x + a.x); } constexpr ModInt operator - (const ModInt& a) const { return ModInt()._set((ll) x - a.x + MD); } constexpr ModInt operator * (const ModInt& a) const { return ModInt()._set((ll) x * a.x % MD); } constexpr ModInt operator / (const ModInt& a) const { return ModInt()._set((ll) x * a.inv().x % MD); } constexpr ModInt operator - () const { return ModInt()._set(MD - x); } constexpr ModInt& operator += (const ModInt& a) { return *this = *this + a; } constexpr ModInt& operator -= (const ModInt& a) { return *this = *this - a; } constexpr ModInt& operator *= (const ModInt& a) { return *this = *this * a; } constexpr ModInt& operator /= (const ModInt& a) { return *this = *this / a; } friend constexpr ModInt operator + (ll a, const ModInt& b) { return ModInt()._set(a % MD + b.x); } friend constexpr ModInt operator - (ll a, const ModInt& b) { return ModInt()._set(a % MD - b.x + MD); } friend constexpr ModInt operator * (ll a, const ModInt& b) { return ModInt()._set(a % MD * b.x % MD); } friend constexpr ModInt operator / (ll a, const ModInt& b) { return ModInt()._set(a % MD * b.inv().x % MD); } constexpr bool operator == (const ModInt& a) const { return x == a.x; } constexpr bool operator != (const ModInt& a) const { return x != a.x; } friend std::istream& operator >> (std::istream& is, ModInt& other) { ll val; is >> val; other = ModInt(val); return is; } constexpr friend std::ostream& operator << (std::ostream& os, const ModInt& other) { return os << other.x; } constexpr ModInt pow(ll k) const { ModInt ans = 1, tmp = x; while (k) { if (k & 1) ans *= tmp; tmp *= tmp; k >>= 1; } return ans; } constexpr ModInt inv() const { if (x < 1000111) { _precalc(1000111); return invs[x]; } int a = x, b = MD, ax = 1, bx = 0; while (b) { int q = a/b, t = a%b; a = b; b = t; t = ax - bx*q; ax = bx; bx = t; } assert(a == 1); if (ax < 0) ax += MD; return ax; } static std::vector<ModInt> factorials, inv_factorials, invs; constexpr static void _precalc(int n) { if (factorials.empty()) { factorials = {1}; inv_factorials = {1}; invs = {0}; } if (n > MD) n = MD; int old_sz = factorials.size(); if (n <= old_sz) return; factorials.resize(n); inv_factorials.resize(n); invs.resize(n); for (int i = old_sz; i < n; ++i) factorials[i] = factorials[i-1] * i; inv_factorials[n-1] = factorials.back().pow(MD - 2); for (int i = n - 2; i >= old_sz; --i) inv_factorials[i] = inv_factorials[i+1] * (i+1); for (int i = n-1; i >= old_sz; --i) invs[i] = inv_factorials[i] * factorials[i-1]; } static int get_primitive_root() { static int primitive_root = 0; if (!primitive_root) { primitive_root = [&]() { std::set<int> fac; int v = MD - 1; for (ll i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i; if (v > 1) fac.insert(v); for (int g = 1; g < MD; g++) { bool ok = true; for (auto i : fac) if (ModInt(g).pow((MD - 1) / i) == 1) { ok = false; break; } if (ok) return g; } return -1; }(); } return primitive_root; } static ModInt C(int n, int k) { _precalc(n + 1); return factorials[n] * inv_factorials[k] * inv_factorials[n-k]; } private: // Internal, DO NOT USE. // val must be in [0, 2*MD) constexpr inline __attribute__((always_inline)) ModInt& _set(ll v) { x = v >= MD ? v - MD : v; return *this; } }; template <int MD> std::vector<ModInt<MD>> ModInt<MD>::factorials = {1}; template <int MD> std::vector<ModInt<MD>> ModInt<MD>::inv_factorials = {1}; template <int MD> std::vector<ModInt<MD>> ModInt<MD>::invs = {0}; // }}} #line 1 "buffered_reader.h" // Buffered reader {{{ namespace IO { const int BUFSIZE = 1<<14; char buf[BUFSIZE + 1], *inp = buf; bool reacheof; char get_char() { if (!*inp && !reacheof) { memset(buf, 0, sizeof buf); int tmp = fread(buf, 1, BUFSIZE, stdin); if (tmp != BUFSIZE) reacheof = true; inp = buf; } return *inp++; } template<typename T> T get() { int neg = 0; T res = 0; char c = get_char(); while (!std::isdigit(c) && c != '-' && c != '+') c = get_char(); if (c == '+') { neg = 0; } else if (c == '-') { neg = 1; } else res = c - '0'; c = get_char(); while (std::isdigit(c)) { res = res * 10 + (c - '0'); c = get_char(); } return neg ? -res : res; } }; // Helper methods int ri() { return IO::get<int>(); } // }}} #line 9 "DataStructure/test/segment_tree_pointsetrangecomposite.test.cpp" using modular = ModInt<998244353>; struct Func { modular a, b; }; Func op(Func l, Func r) { return Func{ l.a * r.a, r.a * l.b + r.b }; } Func e() { return Func{1, 0}; } int32_t main() { ios::sync_with_stdio(0); cin.tie(0); int n = IO::get<int>(); int q = IO::get<int>(); vector<Func> funcs(n); for (auto& f : funcs) { int a = IO::get<int>(); int b = IO::get<int>(); f = {a, b}; } SegTree<Func, op, e> seg_tree(funcs); while (q--) { int typ = IO::get<int>(); if (typ == 0) { int pos = IO::get<int>(); int a = IO::get<int>(); int b = IO::get<int>(); seg_tree.set(pos, {a, b}); } else { int l = IO::get<int>(); int r = IO::get<int>(); auto f = seg_tree.prod(l, r); modular x(IO::get<int>()); cout << f.a * x + f.b << '\n'; } } return 0; }