#include using namespace std; #define NDEBUG #include typedef long long ll; typedef long double Double; typedef unsigned long long ull; typedef pair ii; typedef pair llll; typedef pair dd; typedef vector vi; typedef vector> vvi; typedef vector vii; typedef vector> vvii; typedef vector vll; typedef vector> vvll; typedef vector vllll; typedef vector vb; typedef vector vs; typedef vector vd; typedef vector vD; #define sz(a) int((a).size()) #define pb push_back #define eb emplace_back #define FOR(var,from,to) for(int var=(from);var<=(to);++var) #define rep(var,n) for(int var=0;var<(n);++var) #define rep1(var,n) for(int var=1;var<=(n);++var) #define repC2(vari,varj,n) for(int vari=0;vari<(n)-1;++vari)for(int varj=vari+1;varj<(n);++varj) #define repC3(vari,varj,vark,n) for(int vari=0;vari<(n)-2;++vari)for(int varj=vari+1;varj<(n)-1;++varj)for(int vark=varj+1;vark<(n);++vark) #define ALL(c) (c).begin(),(c).end() #define RALL(c) (c).rbegin(),(c).rend() #define tr(i,c) for(auto i=(c).begin(); i!=(c).end(); ++i) #define found(s,e) ((s).find(e)!=(s).end()) #define mset(arr,val) memset(arr,val,sizeof(arr)) #define mid(x,y) ((x)+((y)-(x))/2) #define IN(x,a,b) ((a)<=(x)&&(x)<=(b)) #define cons make_pair #define clamp(v,lo,hi) min(max(v,lo),hi) template inline void amin(T1 & a, T2 const & b) { if (a>b) a=b; } template inline void amax(T1 & a, T2 const & b) { if (a auto vectors(X x, T a) { return vector(x, a); } template auto vectors(X x, Y y, Z z, Zs... zs) { auto cont = vectors(y, z, zs...); return vector(x, cont); } inline ll square(ll x) { return x * x; } inline ll gcd(ll a, ll b) { while(a) swap(a, b%=a); return b; } template inline T mod(T a, T b) { return ((a % b) + b) % b; } template int find_left(vector& v, T elem) { return (int)(upper_bound(v.begin(), v.end(), elem) - v.begin()) - 1; } template int find_right(vector& v, T elem) { return (int)(lower_bound(v.begin(), v.end(), elem) - v.begin()); } const ll MOD=1000000007LL; inline ll ADD(ll x, ll y) { return (x+y) % MOD; } inline ll SUB(ll x, ll y) { return (x-y+MOD) % MOD; } inline ll MUL(ll x, ll y) { return x*y % MOD; } inline ll POW(ll x, ll e) { ll v=1; for(; e; x=MUL(x,x), e>>=1) if (e&1) v = MUL(v,x); return v; } inline ll INV(ll y) { /*assert(y%MOD!=0);*/ return POW(y, MOD-2); } inline ll DIV(ll x, ll y) { return MUL(x, INV(y)); } #define INTSPACE 12 char _buf[INTSPACE*1000000 + 3]; int loadint() { if (fgets(_buf, INTSPACE+3, stdin)==NULL) return 0; return atoi(_buf); } int loadvec(vector& v, int N=-1) { if (N == 0) { v.clear(); return 0; } if (N == -1) { N = loadint(); if (N==0) return 0; } int bufsize = INTSPACE*N + 3; if (fgets(_buf, bufsize, stdin)==NULL) return 0; v.resize(N); int i=0; bool last = false; for (char *p=&_buf[0]; ;) { char *q = p; while (*q > ' ') ++q; if (*q == 0x0D || *q == 0x0A) last = true; *q = 0; v[i++] = atoi(p); if (last || i == N) break; p = q+1; } return i; } void read_cr() { fgets(_buf, 256, stdin); } template class LazySegmentTree { public: Elem (*f)(Elem& a, Elem& b); void (*g)(Elem& a, LazyOperand& b); void (*h)(LazyOperand& a, LazyOperand& b); using fTYPE = decltype(f); using gTYPE = decltype(g); using hTYPE = decltype(h); Elem elem_ident; LazyOperand lazy_operand_ident; vector elems; vector lazy_operands; int n, height; LazySegmentTree(fTYPE f, gTYPE g, hTYPE h, Elem elem_ident, LazyOperand lazy_operand_ident) : f(f), g(g), h(h), elem_ident(elem_ident), lazy_operand_ident(lazy_operand_ident) {} void init(int n_temp) { n = 1; height = 0; while (n < n_temp) { n <<= 1; ++height; } elems.assign(2*n, elem_ident); lazy_operands.assign(2*n, lazy_operand_ident); } void build(const vector& v){ int n_temp = v.size(); init(n_temp); rep(i,n_temp) elems[n+i] = v[i]; for (int i=n-1; i>0; --i) { elems[i] = (*f)(elems[i*2], elems[i*2+1]); } } inline void assign_merged_lazy(int dest, LazyOperand& x) { (*h)(lazy_operands[dest], x); } inline void reflect(int k){ if (lazy_operands[k] != lazy_operand_ident) { (*g)(elems[k], lazy_operands[k]); } } inline void _eval(int k){ if (lazy_operands[k] != lazy_operand_ident) { assign_merged_lazy(k*2, lazy_operands[k]); assign_merged_lazy(k*2+1, lazy_operands[k]); /*elems[k] =*/ reflect(k); lazy_operands[k] = lazy_operand_ident; } } inline void eval_down(int k) { for (int i=height; i>0; --i) { _eval(k >> i); } } inline void recalc(int k) { while (k >>= 1) { reflect(k*2); reflect(k*2+1); elems[k] = (*f)(elems[k*2], elems[k*2+1]); } } void update(int a, int b, LazyOperand& x) { a += n; b += n; eval_down(a); eval_down(b-1); for (int l=a,r=b; l>=1,r>>=1) { if (l & 1) assign_merged_lazy(l++, x); if (r & 1) assign_merged_lazy(--r, x); } recalc(a); recalc(b-1); } void set_val(int a, Elem e) { a += n; eval_down(a); elems[a] = e; lazy_operands[a] = lazy_operand_ident; recalc(a); } Elem query(int a, int b) { a += n; b += n; eval_down(a); eval_down(b-1); Elem vl = elem_ident, vr = elem_ident; for (int l=a,r=b; l>=1,r>>=1) { if (l & 1) { reflect(l); vl = (*f)(vl, elems[l]); ++l; } if (r & 1) { --r; reflect(r); vr = (*f)(elems[r], vr); } } return move((*f)(vl, vr)); } void desc() { } }; template class MyLazySegTree { using Map = unordered_map; using Elem = pair, Map>; using LazyOp = pair; using LazyOperand = vector; using Monoid = pair; static Monoid f(Monoid& a, Monoid& b) { Monoid res; for (auto& p: a.first.second) { res.first.second[p.first] += p.second; res.first.first.first += p.first * p.second; amax(res.first.first.second, p.first); } for (auto& p: b.first.second) { res.first.second[p.first] += p.second; res.first.first.first += p.first * p.second; amax(res.first.first.second, p.first); } res.second = a.second + b.second; return move(res); } static void g(Monoid& a, LazyOperand& b) { int mag = a.second; for (LazyOp& op: b) { T k = op.second; if (op.first) { a.first.second.clear(); a.first.second[k] = mag; a.first.first.first = k*mag; a.first.first.second = k; } else { Map tmp; a.first.first.first = a.first.first.second = 0; for (auto& p: a.first.second) { T g = gcd(p.first, k); tmp[g] += p.second; a.first.first.first += g * p.second; amax(a.first.first.second, g); } a.first.second = tmp; } } } static void h(LazyOperand& a, LazyOperand& b) { int al = a.size(), bl = b.size(); int a_assign = -1; rep(i,al){ if (a[i].first) { a_assign = i; break; } } rep(i,bl){ if (b[i].first) { a.assign(1, b[i]); } else { if (!a.empty() && !a.back().first) { a.back().second = gcd(a.back().second, b[i].second); } else { a.pb(b[i]); } } } } public: LazySegmentTree *st = nullptr; public: MyLazySegTree(int size) { this->st = new LazySegmentTree( &f, &g, &h, Monoid(Elem(),1), vector() ); this->st->build(vector(size, Monoid(Elem(),1))); } MyLazySegTree(vector& ar) { this->st = new LazySegmentTree( &f, &g, &h, Monoid(Elem(),1), vector() ); vector tmp(ar.size()); rep(i, ar.size()) { tmp[i] = Monoid(Elem(make_pair(ar[i], ar[i]), {{ar[i], 1}}), 1); } this->st->build(tmp); } virtual ~MyLazySegTree() { if (st != nullptr) delete st; } public: void assign(int l, int r, T x) { LazyOperand op { LazyOp(1,x) }; st->update(l, r, op); } void update_gcd(int l, int r, T x){ LazyOperand op { LazyOp(0,x) }; st->update(l, r, op); } T query_sum(int l, int r) { return st->query(l, r).first.first.first; } T query_max(int l, int r) { return st->query(l, r).first.first.second; } }; inline vll vi2vll(vi& orig) { int L = orig.size(); vll dest(L); rep(i, L) dest[i] = (ll)orig[i]; return dest; } int main() { int N, Q; scanf("%d %d%*c", &N, &Q); vi a(N); loadvec(a,N); vll aLL = vi2vll(a); MyLazySegTree st(aLL); rep(i,Q){ int op, l, r, x; scanf("%d ", &op); switch (op) { case 1: { scanf("%d %d %d%*c", &l, &r, &x); --l; st.assign(l, r, x); break; } case 2: { scanf("%d %d %d%*c", &l, &r, &x); --l; st.update_gcd(l, r, x); break; } case 3: { scanf("%d %d%*c", &l, &r); --l; ll y = st.query_max(l, r); printf("%lld\n", y); break; } case 4: { scanf("%d %d%*c", &l, &r); --l; ll y = st.query_sum(l, r); printf("%lld\n", y); break; } } } return 0; }