#ifndef ONLINE_JUDGE #define _GLIBCXX_DEBUG #endif #include using namespace std; #define pass (void)0 #define INF (1<<30)-1 #define INFLL (1LL<<60)-1 #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define repr(i, n) for (int i = (int)(n) - 1; i >= 0; i--) #define rep2(i, a, b) for (int i = (int)(a); i < (int)(b); i++) #define repr2(i, a, b) for (int i = (int)(b) - 1; i >= (int)(a); i--) #define all(x) (x).begin(), (x).end() #define rall(x) (x).rbegin(), (x).rend() #define sz(x) ((int)(x).size()) #define YesNo(cond) cout << ((cond) ? "Yes\n" : "No\n") #define YESNO(cond) cout << ((cond) ? "YES\n" : "NO\n") using ll = long long; using pii = pair; using pll = pair; using vi = vector; using vl = vector; using vvi = vector; using vvl = vector; template void print(const T& value) { cout << value << "\n"; } template void print(const vector& vec) { for (auto& v : vec) cout << v << " "; cout << "\n"; } template void input(vector& vec) { for (auto& v : vec) cin >> v; }; template bool chmin(T& a, const T& b) { if (a > b) { a = b; return true; } return false; } template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } return false; } 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 template struct lazy_segtree { public: lazy_segtree() : lazy_segtree(0) {} lazy_segtree(int n) : lazy_segtree(std::vector(n, e())) {} 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); } } void push(int k) { all_apply(2 * k, lz[k]); all_apply(2 * k + 1, lz[k]); lz[k] = id(); } }; struct Node { ll MAX; ll SUM; ll LCM; ll size; bool fail; }; Node op(Node left, Node right) { return {max(left.MAX, right.MAX), left.SUM+right.SUM, min(lcm(left.LCM, right.LCM), (ll)INF), left.size+right.size}; } Node e() { return {0, 0, 1, 0}; } struct Lazy { ll val; ll gval; }; Node mapping(Lazy top, Node bottom) { if (bottom.fail) return bottom; if (top.val != 0) { auto nex = gcd(top.val, top.gval); bottom.MAX = nex; bottom.SUM = nex*bottom.size; bottom.LCM = nex; return bottom; } if (bottom.MAX*bottom.size == bottom.SUM) { auto nex = gcd(bottom.MAX, top.gval); bottom.MAX = nex; bottom.SUM = nex*bottom.size; bottom.LCM = nex; return bottom; } if (top.gval%bottom.LCM == 0) { return bottom; } bottom.fail = true; return bottom; } Lazy composition(Lazy top, Lazy bottom) { if (top.val != 0) { bottom.val = top.val; bottom.gval = 0; } bottom.gval = gcd(bottom.gval, top.gval); return bottom; } Lazy ID() { return {0, 0}; } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(10); ll N, Q; cin >> N >> Q; vl A(N); input(A); vector def(N); rep (i, N) def[i] = {A[i], A[i], A[i], 1, false}; lazy_segtree seg(def); while (Q--) { ll t, l, r; cin >> t >> l >> r; l --; r --; if (t == 1) { ll x; cin >> x; seg.apply(l, r+1, {x, 0}); } else if (t == 2) { ll x; cin >> x; seg.apply(l, r+1, {0, x}); } else if (t == 3) { auto res = seg.prod(l, r+1); print(res.MAX); } else { auto res = seg.prod(l, r+1); print(res.SUM); } } }