#include using namespace std; // [ SEGMENT TREE BEATS ] BY SHOBON // REFERENCE --- ATCODER LIBRARY, HITONANODE // VERSION 1.0 (2024/02/14) int ceil_pow2(int n) { int x = 0; while ((1U << x) < (unsigned int)(n)) x++; return x; } 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 = 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(); } }; // ---- END : SEGMENT TREE BEATS ---- typedef long long ll; ll INF = 2e9; struct S{ int max_val; int lcm; int len; ll sum; bool fail; }; S e(){ return {0, 1, 0, 0, false}; } S apply_reset(S original, int x){ return {x, x, original.len, (ll)original.len * x, false}; } S op(S l, S r){ if (r.len == 0) return l; if (l.len == 0) return r; S ret = e(); ret.max_val = max(l.max_val, r.max_val); ret.lcm = min(INF, (ll)l.lcm * r.lcm / __gcd(l.lcm, r.lcm)); ret.len = l.len + r.len; ret.sum = l.sum + r.sum; return ret; } struct F{ int dogcd; int reset; }; F id(){ return {0, 0}; } S mapping(F f, S x){ if (x.fail) return x; assert(!((f.reset > 0) && (f.dogcd > 0))); if (f.reset > 0){ return apply_reset(x, f.reset); } if (f.dogcd > 0){ if (x.len == 1){ // always success if the length is 1. return apply_reset(x, __gcd(f.dogcd, x.max_val)); } // if there is some i (0 <= i < n) such that // __gcd(g, x[i]) < x[i], then g % x[i] > 0 so g % lcm(x) > 0 // conversely if g % lcm(x) > 0 => exists i s.t. __gcd(g, x[i]) < x[i] // follows. if (x.lcm == INF || f.dogcd % x.lcm > 0){ x.fail = 1; return x; } } // no change return x; } F composition(F g, F f){ if (g.reset){ return {0, g.reset}; } if (f.reset){ return {0, __gcd(g.dogcd, f.reset)}; } return {__gcd(g.dogcd, f.dogcd), 0}; } int main(){ ios_base::sync_with_stdio(false); cin.tie(NULL); int n, q; cin >> n >> q; vector a(n); vector inits(n); for (int i=0; i> a[i]; inits[i] = apply_reset({0, 1, 1, 0}, a[i]); } segtree_beats seg(inits); while(q--){ int t; cin >> t; int l, r; cin >> l >> r; l--; if (t == 1){ ll x; cin >> x; seg.apply(l, r, {0, x}); }else if(t == 2){ ll x; cin >> x; seg.apply(l, r, {x, 0}); }else if(t == 3){ cout << seg.prod(l, r).max_val << '\n'; }else if(t == 4){ cout << seg.prod(l, r).sum << '\n'; }else{ assert(false); } } }