#include namespace { #pragma GCC diagnostic push #pragma GCC diagnostic ignored "-Wunused-function" #include #pragma GCC diagnostic pop using namespace std; using namespace atcoder; #define rep(i,n) for(int i = 0; i < (int)(n); i++) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--) #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; } using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; template struct segtree_beats { public: segtree_beats() : segtree_beats(0) {} explicit segtree_beats(int n) : segtree_beats(std::vector(n, e())) {} explicit segtree_beats(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 - 1) >> 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) { if (k < size) { lz[k] = composition(f, lz[k]); if (mappable(f, d[k])) { d[k] = mapping(f, d[k]); } else { push(k); update(k); } } else { d[k] = mapping(f, d[k]); } } void push(int k) { all_apply(2 * k, lz[k]); all_apply(2 * k + 1, lz[k]); lz[k] = id(); } }; constexpr int INF = 1001002001; struct S { int cnt; ll sm; int mx; int l; bool same; }; S e() { return {0, 0, 0, 1, true}; } S op(S x, S y) { if (!x.cnt) return y; if (!y.cnt) return x; int g = gcd(x.l, y.l); int l; if (__builtin_mul_overflow(x.l / g, y.l, &l)) l = INF; return { x.cnt + y.cnt, x.sm + y.sm, max(x.mx, y.mx), l, x.same && y.same && x.mx == y.mx }; } using F = int; // negarive->assign, non-negative->gcd F id() { return 0; } F composition(F f, F g) { if (f < 0) return f; if (g < 0) return -gcd(g, f); return gcd(f, g); } bool mappable(F f, S x) { if (f < 0) return true; if (f % x.l == 0) return true; if (x.same) return true; return false; } S mapping(F f, S x) { if (f < 0) return {x.cnt, (ll)x.cnt * -f, -f, -f, true}; if (f % x.l == 0) return x; // x.same int nmx = gcd(x.mx, f); return {x.cnt, (ll)x.cnt * nmx, nmx, nmx, true}; } } int main() { ios::sync_with_stdio(false); cin.tie(0); int n, q; cin >> n >> q; vector init_vec(n); rep(i, n) { int x; cin >> x; init_vec[i] = {1, x, x, x, true}; } segtree_beats seg(init_vec); while(q--) { int t, l, r; cin >> t >> l >> r; l--; if (t == 1) { int x; cin >> x; seg.apply(l, r, -x); } else if (t == 2) { int x; cin >> x; seg.apply(l, r, x); } else if (t == 3) { cout << seg.prod(l, r).mx << '\n'; } else { cout << seg.prod(l, r).sm << '\n'; } } }