#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 all_same; // 区間内全要素が同一の値のときのみ true となるフラグ bool fail; S() : max(0), lcm(1), sz(1), sum(0), all_same(0), fail(0) {} S(uint32_t x, uint32_t sz_ = 1) : max(x), lcm(x), sz(sz_), sum((uint64_t)x * sz_), all_same(1), 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; if (l.all_same and r.all_same and l.max == r.max) ret.all_same = true; 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) { return fnew.reset ? fnew : F(std::__gcd(fnew.dogcd, fold.dogcd), fold.reset); } 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.all_same) { x = S(std::__gcd(f.dogcd, x.max), x.sz); } else if (f.dogcd and (x.lcm == BINF or f.dogcd % x.lcm)) { // 区間 gcd クエリによって,複数の値が異なる要素が変更を受けう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, 1}; } 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'; } } }