#include using ll = long long; using ld = long double; #define rep(i, l, r) for (ll i = (l); i < (r); i++) #define rrep(i, r, l) for (ll i = (r); i-- > (l);) #define all(x) begin(x), end(x) template bool chmin(T& lhs, T rhs) { return lhs > rhs ? (lhs = rhs, true) : false; } template bool chmax(T& lhs, T rhs) { return lhs < rhs ? (lhs = rhs, true) : false; } struct IOIO { IOIO() { std::cin.tie(0)->sync_with_stdio(0); } } ioio; using namespace std; #include using namespace std; template ostream& operator<<(ostream& os, const vector& vs) { os << '{'; rep(i, 0, (int)vs.size()) os << vs[i] << (i + 1 == (int)vs.size() ? "" : ", "); os << '}'; return os; } template ostream& operator<<(ostream& os, const pair& p) { os << '(' << p.first << ", " << p.second << ')'; return os; } #ifdef DEBUG #define dump(x) cerr << "[" + string(#x) + "] " << x << endl; #else #define dump(...) #endif template struct segment_tree_beats { using T = M::T; using F = M::F; int n; vector a; vector lz; segment_tree_beats(int n_): n(bit_ceil((unsigned)n_)), a(2 * n, M::e()), lz(n, M::id()) {} segment_tree_beats(const vector& a_): n(bit_ceil(a_.size())), a(2 * n, M::e()), lz(n, M::id()) { copy(all(a_), a.begin() + n); rrep(i, n, 1) update(i); } void apply(int l, int r, F v) { apply(0, n, l, r, 1, v); } T prod(int l, int r) { return prod(0, n, l, r, 1); } T get(int i) { return prod(0, n, i, i + 1, 1); } friend ostream& operator<<(ostream& os, segment_tree_beats& s) { rep(i, 0, s.n) s.get(i); os << vector(s.a.begin() + s.n, s.a.end()); return os; } private: void apply(int l, int r, int L, int R, int i, F v) { if (r <= L || R <= l) return; int m = (l + r) / 2; if (L <= l && r <= R) { eval(i, v); } else { push(i); apply(l, m, L, R, 2 * i, v); apply(m, r, L, R, 2 * i + 1, v); update(i); } } T prod(int l, int r, int L, int R, int i) { if (r <= L || R <= l) return M::e(); int m = (l + r) / 2; if (L <= l && r <= R) { return a[i]; } else { push(i); T p = M::op(prod(l, m, L, R, 2 * i), prod(m, r, L, R, 2 * i + 1)); return p; } } void push(int i) { eval(2 * i, lz[i]); eval(2 * i + 1, lz[i]); lz[i] = M::id(); } void update(int i) { a[i] = M::op(a[2 * i], a[2 * i + 1]); } void eval(int i, F v) { a[i] = M::map(v, a[i]); if (i < n) { lz[i] = M::compose(v, lz[i]); if (a[i].fail) { push(i); update(i); } } } }; template struct update_gcd_max_sum { static constexpr U update_id = numeric_limits::min(); static constexpr U gcd_id = 0; static constexpr U inf = U(1e9) + 5; struct ope { U a, b; ope(U a, U b): a(a), b(b) {} static ope update(U a) { return ope(a, gcd_id); } static ope gcd(U b) { return ope(update_id, b); } }; struct info { info() {} info(U v): s(v), x(v), n(1), l(v), fail(false), same(true) {} U s, x, n, l; bool fail; bool same; friend ostream& operator<<(ostream& os, info i) { os << i.s; return os; } }; using T = info; using F = ope; static T op(T lhs, T rhs) { lhs.same &= rhs.same && lhs.x == rhs.x; lhs.s += rhs.s; chmax(lhs.x, rhs.x); lhs.n += rhs.n; lhs.l = min(lcm(lhs.l, rhs.l), inf); return lhs; } static T e() { T a; a.s = 0; a.x = -inf; a.n = 0; a.l = 1; a.fail = false; return a; } static T map(F lhs, T rhs) { if (lhs.a != update_id) { rhs.x = lhs.a; rhs.l = lhs.a; rhs.s = rhs.n * lhs.a; } if (lhs.b % rhs.l == 0) return rhs; if (rhs.same) { rhs.x = rhs.l = rhs.s = gcd(rhs.x, lhs.b) + rhs.n; return rhs; } rhs.fail = true; return rhs; } static F compose(F lhs, F rhs) { if (lhs.a != update_id) return lhs; return F(rhs.a, gcd(lhs.b, rhs.b)); } static F id() { return F(update_id, gcd_id); } }; int main() { int n, q; cin >> n >> q; using info = update_gcd_max_sum::info; using ope = update_gcd_max_sum::ope; vector a(n); rep(i, 0, n) { ll v; cin >> v; a[i] = info(v); } segment_tree_beats> segtree(a); dump(segtree); rep(_, 0, q) { int t; cin >> t; if (t == 1) { int l, r; ll x; cin >> l >> r >> x; l--; segtree.apply(l, r, ope::update(x)); } else if (t == 2) { int l, r; ll x; cin >> l >> r >> x; l--; segtree.apply(l, r, ope::gcd(x)); } else if (t == 3) { int l, r; cin >> l >> r; l--; cout << segtree.prod(l, r).x << '\n'; } else { int l, r; cin >> l >> r; l--; cout << segtree.prod(l, r).s << '\n'; } dump(segtree); } }