#define PROBLEM "https://yukicoder.me/problems/no/880" #include #include #include #include #include #include #include namespace suisen { template using constraints_t = std::enable_if_t, std::nullptr_t>; template struct bitnum { static constexpr int value = 0; }; template struct bitnum>> { static constexpr int value = std::numeric_limits>::digits; }; template static constexpr int bitnum_v = bitnum::value; template struct is_nbit { static constexpr bool value = bitnum_v == n; }; template static constexpr bool is_nbit_v = is_nbit::value; template struct safely_multipliable { using type = T; }; template struct safely_multipliable, is_nbit>> { using type = long long; }; template struct safely_multipliable, is_nbit>> { using type = __int128_t; }; template struct safely_multipliable, is_nbit>> { using type = unsigned long long; }; template struct safely_multipliable, is_nbit>> { using type = __uint128_t; }; template using safely_multipliable_t = typename safely_multipliable::type; template struct rec_value_type { using type = T; }; template struct rec_value_type> { using type = typename rec_value_type::type; }; template using rec_value_type_t = typename rec_value_type::type; template class is_iterable { template static auto test(T_ e) -> decltype(e.begin(), e.end(), std::true_type{}); static std::false_type test(...); public: static constexpr bool value = decltype(test(std::declval()))::value; }; template static constexpr bool is_iterable_v = is_iterable::value; template class is_writable { template static auto test(T_ e) -> decltype(std::declval() << e, std::true_type{}); static std::false_type test(...); public: static constexpr bool value = decltype(test(std::declval()))::value; }; template static constexpr bool is_writable_v = is_writable::value; template class is_readable { template static auto test(T_ e) -> decltype(std::declval() >> e, std::true_type{}); static std::false_type test(...); public: static constexpr bool value = decltype(test(std::declval()))::value; }; template static constexpr bool is_readable_v = is_readable::value; } // namespace suisen namespace suisen { template > = nullptr> struct UpdateProxyObject { public: UpdateProxyObject(T &v, UpdateFunc update) : v(v), update(update) {} operator T() const { return v; } auto& operator++() && { ++v, update(); return *this; } auto& operator--() && { --v, update(); return *this; } auto& operator+=(const T &val) && { v += val, update(); return *this; } auto& operator-=(const T &val) && { v -= val, update(); return *this; } auto& operator*=(const T &val) && { v *= val, update(); return *this; } auto& operator/=(const T &val) && { v /= val, update(); return *this; } auto& operator%=(const T &val) && { v %= val, update(); return *this; } auto& operator =(const T &val) && { v = val, update(); return *this; } auto& operator<<=(const T &val) && { v <<= val, update(); return *this; } auto& operator>>=(const T &val) && { v >>= val, update(); return *this; } template > = nullptr> auto& apply(F f) && { v = f(v), update(); return *this; } private: T &v; UpdateFunc update; }; } // namespace suisen namespace suisen { template struct LazySegmentTree { using value_type = T; using operator_type = F; LazySegmentTree() : LazySegmentTree(0) {} LazySegmentTree(int n) : LazySegmentTree(std::vector(n, e())) {} LazySegmentTree(const std::vector& init) : n(init.size()), m(ceil_pow2(n)), lg(__builtin_ctz(m)), data(2 * m, e()), lazy(m, id()) { std::copy(init.begin(), init.end(), data.begin() + m); for (int k = m - 1; k > 0; --k) update(k); } void apply(int l, int r, const operator_type& f) { assert(0 <= l and l <= r and r <= n); push_to(l, r); for (int l2 = l + m, r2 = r + m; l2 < r2; l2 >>= 1, r2 >>= 1) { if (l2 & 1) all_apply(l2++, f); if (r2 & 1) all_apply(--r2, f); } update_from(l, r); } void apply(int p, const operator_type& f) { (*this)[p] = mapping(f, get(p)); } value_type operator()(int l, int r) { assert(0 <= l and l <= r and r <= n); push_to(l, r); value_type res_l = e(), res_r = e(); for (l += m, r += m; l < r; l >>= 1, r >>= 1) { if (l & 1) res_l = op(res_l, data[l++]); if (r & 1) res_r = op(data[--r], res_r); } return op(res_l, res_r); } value_type prod(int l, int r) { return (*this)(l, r); } value_type prefix_prod(int r) { return (*this)(0, r); } value_type suffix_prod(int l) { return (*this)(l, m); } value_type all_prod() const { return data[1]; } auto operator[](int p) { assert(0 <= p and p < n); push_to(p); return UpdateProxyObject{ data[p + m], [this, p] { update_from(p); } }; } value_type get(int p) { return (*this)[p]; } void set(int p, value_type v) { (*this)[p] = v; } template > = nullptr> int max_right(int l, Pred g) { assert(0 <= l && l <= n); assert(g(e())); if (l == n) return n; l += m; for (int i = lg; i >= 1; --i) push(l >> i); value_type sum = e(); do { while ((l & 1) == 0) l >>= 1; if (not g(op(sum, data[l]))) { while (l < m) { push(l); l = 2 * l; if (g(op(sum, data[l]))) sum = op(sum, data[l++]); } return l - m; } sum = op(sum, data[l++]); } while ((l & -l) != l); return n; } template int max_right(int l) { return max_right(l, f); } template > = nullptr> int min_left(int r, Pred g) { assert(0 <= r && r <= n); assert(g(e())); if (r == 0) return 0; r += m; for (int i = lg; i >= 1; --i) push(r >> i); value_type sum = e(); do { r--; while (r > 1 and (r & 1)) r >>= 1; if (not g(op(data[r], sum))) { while (r < m) { push(r); r = 2 * r + 1; if (g(op(data[r], sum))) sum = op(data[r--], sum); } return r + 1 - m; } sum = op(data[r], sum); } while ((r & -r) != r); return 0; } template int min_left(int l) { return min_left(l, f); } private: int n, m, lg; std::vector data; std::vector lazy; static constexpr int ceil_pow2(int n) { int m = 1; while (m < n) m <<= 1; return m; } void all_apply(int k, const operator_type& f) { data[k] = mapping(f, data[k]); if (k < m) { lazy[k] = composition(f, lazy[k]); if constexpr (enable_beats) if (data[k].fail) push(k), update(k); } } void push(int k) { all_apply(2 * k, lazy[k]), all_apply(2 * k + 1, lazy[k]); lazy[k] = id(); } void push_to(int p) { p += m; for (int i = lg; i >= 1; --i) push(p >> i); } void push_to(int l, int r) { l += m, r += m; int li = __builtin_ctz(l), ri = __builtin_ctz(r); for (int i = lg; i >= li + 1; --i) push(l >> i); for (int i = lg; i >= ri + 1; --i) push(r >> i); } void update(int k) { data[k] = op(data[2 * k], data[2 * k + 1]); } void update_from(int p) { p += m; for (int i = 1; i <= lg; ++i) update(p >> i); } void update_from(int l, int r) { l += m, r += m; int li = __builtin_ctz(l), ri = __builtin_ctz(r); for (int i = li + 1; i <= lg; ++i) update(l >> i); for (int i = ri + 1; i <= lg; ++i) update(r >> i); } }; } namespace suisen { template using SegmentTreeBeats = LazySegmentTree; } // namespace suisen constexpr long long inf = 2000000000; struct S { long long sum_v; int max_v; long long lcm_v; int siz; bool fail = false; S(long long sum_v, int max_v, long long lcm_v, int siz) : sum_v(sum_v), max_v(max_v), lcm_v(lcm_v), siz(siz) {} S(int v) : sum_v(v), max_v(v), lcm_v(v), siz(1) {} S() = default; }; struct F { int upd_v = 0; int gcd_v = 0; F(int upd_v = 0, int gcd_v = 0) : upd_v(upd_v), gcd_v(gcd_v) {} static F upd_query(int upd_v) { return F { upd_v, 0 }; } static F gcd_query(int gcd_v) { return F { 0, gcd_v }; } }; S op(S x, S y) { return S { x.sum_v + y.sum_v, std::max(x.max_v, y.max_v), std::min(std::lcm(x.lcm_v, y.lcm_v), inf), x.siz + y.siz }; } S e() { return S { 0LL, 0, 1, 0 }; } S mapping(F f, S x) { if (x.fail) return x; if (f.upd_v) return S { (long long) f.upd_v * x.siz, f.upd_v, f.upd_v, x.siz }; if (f.gcd_v) { if (x.siz == 1) { return S { std::gcd(x.max_v, f.gcd_v) }; } else if (x.lcm_v == inf or f.gcd_v % x.lcm_v) { x.fail = true; } } return x; } F composition(F f, F g) { if (f.upd_v) return f; if (g.upd_v) return F::upd_query(std::gcd(g.upd_v, f.gcd_v)); return F::gcd_query(std::gcd(f.gcd_v, g.gcd_v)); } F id() { return F::gcd_query(0); } int main() { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); int n, q; std::cin >> n >> q; std::vector init(n); for (int i = 0; i < n; ++i) { int v; std::cin >> v; init[i] = S{v}; } suisen::SegmentTreeBeats seg(init); while (q --> 0) { int qt; std::cin >> qt; if (qt == 1) { int l, r, x; std::cin >> l >> r >> x; --l; seg.apply(l, r, F::upd_query(x)); } else if (qt == 2) { int l, r, x; std::cin >> l >> r >> x; --l; seg.apply(l, r, F::gcd_query(x)); } else if (qt == 3) { int l, r; std::cin >> l >> r; --l; std::cout << seg.prod(l, r).max_v << '\n'; } else { int l, r; std::cin >> l >> r; --l; std::cout << seg.prod(l, r).sum_v << '\n'; } } return 0; }