#ifndef ATCODER_LAZYSEGTREE_HPP #define ATCODER_LAZYSEGTREE_HPP 1 #include #include #include #include // #include "atcoder/internal_bit" #ifndef ATCODER_INTERNAL_BITOP_HPP #define ATCODER_INTERNAL_BITOP_HPP 1 #ifdef _MSC_VER #include #endif namespace atcoder { namespace internal { // @param n `0 <= n` // @return minimum non-negative `x` s.t. `n <= 2**x` int ceil_pow2(int n) { int x = 0; while ((1U << x) < (unsigned int)(n)) x++; return x; } // @param n `1 <= n` // @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0` int bsf(unsigned int n) { #ifdef _MSC_VER unsigned long index; _BitScanForward(&index, n); return index; #else return __builtin_ctz(n); #endif } } // namespace internal } // namespace atcoder #endif // ATCODER_INTERNAL_BITOP_HPP namespace atcoder { template struct lazy_segtree { public: lazy_segtree() : lazy_segtree(0) {} explicit lazy_segtree(int n) : lazy_segtree(std::vector(n, e())) {} explicit lazy_segtree(const std::vector& v) : _n(int(v.size())) { log = internal::ceil_pow2(_n); size = 1 << log; d = std::vector(2 * size, e()); lz = std::vector(size, id()); for (int i = 0; i < _n; i++) d[size + i] = v[i]; for (int i = size - 1; i >= 1; i--) { update(i); } } void set(int p, S x) { assert(0 <= p && p < _n); p += size; for (int i = log; i >= 1; i--) push(p >> i); d[p] = x; for (int i = 1; i <= log; i++) update(p >> i); } S get(int p) { assert(0 <= p && p < _n); p += size; for (int i = log; i >= 1; i--) push(p >> i); return d[p]; } S prod(int l, int r) { assert(0 <= l && l <= r && r <= _n); if (l == r) return e(); l += size; r += size; for (int i = log; i >= 1; i--) { if (((l >> i) << i) != l) push(l >> i); if (((r >> i) << i) != r) push(r >> i); } S sml = e(), smr = e(); 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); } S all_prod() { return d[1]; } void apply(int p, F f) { assert(0 <= p && p < _n); p += size; for (int i = log; i >= 1; i--) push(p >> i); d[p] = mapping(f, d[p]); for (int i = 1; i <= log; i++) update(p >> i); } void apply(int l, int r, F f) { assert(0 <= l && l <= r && r <= _n); if (l == r) return; l += size; r += size; for (int i = log; i >= 1; i--) { if (((l >> i) << i) != l) push(l >> i); if (((r >> i) << i) != r) push((r - 1) >> i); } { int l2 = l, r2 = r; while (l < r) { if (l & 1) all_apply(l++, f); if (r & 1) all_apply(--r, f); l >>= 1; r >>= 1; } l = l2; r = r2; } for (int i = 1; i <= log; i++) { if (((l >> i) << i) != l) update(l >> i); if (((r >> i) << i) != r) update((r - 1) >> i); } } template int max_right(int l) { return max_right(l, [](S x) { return g(x); }); } template int max_right(int l, G g) { assert(0 <= l && l <= _n); assert(g(e())); if (l == _n) return _n; l += size; for (int i = log; i >= 1; i--) push(l >> i); S sm = e(); do { while (l % 2 == 0) l >>= 1; if (!g(op(sm, d[l]))) { while (l < size) { push(l); l = (2 * l); if (g(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; } template int min_left(int r) { return min_left(r, [](S x) { return g(x); }); } template int min_left(int r, G g) { assert(0 <= r && r <= _n); assert(g(e())); if (r == 0) return 0; r += size; for (int i = log; i >= 1; i--) push((r - 1) >> i); S sm = e(); do { r--; while (r > 1 && (r % 2)) r >>= 1; if (!g(op(d[r], sm))) { while (r < size) { push(r); r = (2 * r + 1); if (g(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; std::vector d; std::vector lz; void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); } void all_apply(int k, F f) { d[k] = mapping(f, d[k]); if (k < size) { lz[k] = composition(f, lz[k]); if (d[k].fail) push(k), update(k); // MODIFIED!!! } } void push(int k) { all_apply(2 * k, lz[k]); all_apply(2 * k + 1, lz[k]); lz[k] = id(); } }; } // namespace atcoder #endif // ATCODER_LAZYSEGTREE_HPP /////////////////////////////////////////////////////// ACL ここまで /////////////////////////////////////////////////////// namespace RangeUpdateChgcdRangeMaxSum { constexpr uint32_t BINF = 1 << 30; struct S { uint32_t max; // 区間最大値 uint32_t lcm; // min(BINF, (区間内全要素の最大公約数)) uint32_t sz; // 区間要素数 uint64_t sum; // 区間内全要素の総和 bool fail; S() : max(0), lcm(1), sz(0), sum(0), fail(0) {} S(uint32_t x, uint32_t sz_ = 1) : max(x), lcm(x), sz(sz_), sum((uint64_t)x * sz_), fail(0) {} }; S e() { return S(); } S op(S l, S r) { if (r.sz == 0) return l; if (l.sz == 0) return r; S ret; ret.max = std::max(l.max, r.max); ret.sum = l.sum + r.sum; ret.lcm = std::min(uint64_t(BINF), (uint64_t)l.lcm * r.lcm / std::__gcd(l.lcm, r.lcm)); ret.sz = l.sz + r.sz; return ret; } struct F { uint32_t dogcd, reset; F() : dogcd(0), reset(0) {} F(uint32_t g, uint32_t upd) : dogcd(g), reset(upd) {} static F gcd(uint32_t g) noexcept { return F(g, 0); } static F update(uint32_t a) noexcept { return F(0, a); } }; F composition(F fnew, F fold) { if (fnew.reset) return F::update(fnew.reset); else if (fold.reset) { return F::update(std::__gcd(fnew.dogcd, fold.reset)); } else { return F::gcd(std::__gcd(fnew.dogcd, fold.dogcd)); } } F id() { return F(); } S mapping(F f, S x) { if (x.fail) return x; if (f.reset) x = S(f.reset, x.sz); if (f.dogcd) { if (x.sz == 1) { x = S(std::__gcd(x.max, f.dogcd)); } else if (x.lcm == BINF or f.dogcd % x.lcm) { // 区間 gcd クエリによって,複数個の要素からなる区間である値が変更を受ける場合のみ計算失敗 x.fail = true; } } return x; } using segtree = atcoder::lazy_segtree; } // namespace RangeUpdateChgcdRangeMaxSum #include using namespace std; int main() { cin.tie(nullptr), ios::sync_with_stdio(false); uint32_t N, Q; cin >> N >> Q; vector A(N); for (auto &a : A) { uint32_t tmp; cin >> tmp, a = tmp; } RangeUpdateChgcdRangeMaxSum::segtree segtree(A); uint32_t q, l, r, x; while (Q--) { cin >> q >> l >> r; l--; if (q <= 2) { cin >> x; if (q == 1) segtree.apply(l, r, RangeUpdateChgcdRangeMaxSum::F::update(x)); if (q == 2) segtree.apply(l, r, RangeUpdateChgcdRangeMaxSum::F::gcd(x)); } else { auto v = segtree.prod(l, r); if (q == 3) cout << v.max << '\n'; if (q == 4) cout << v.sum << '\n'; } } }