This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#define int ll
using namespace std;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define rng(i,c,n) for(int i=c;i<n;i++)
#define fi first
#define se second
#define pb push_back
#define sz(a) (int)a.size()
#define vec(...) vector<__VA_ARGS__>
#define _3xaMC2q ios::sync_with_stdio(0),cin.tie(0)
typedef long long ll;
using pii=pair<int,int>;
using vi=vector<int>;
void print(){cout<<'\n';}
template<class h,class...t>
void print(const h&v,const t&...u){cout<<v<<' ',print(u...);}
//e
using vp=vec(pii);
struct N{
int val,len;
vp fr,bk;
N(int _val=0,int _len=0,vp vc={}):
val(_val),len(_len),fr(vc),bk(vc){}
};
int f(int si,int n){
return si*n-(n*(n-1))/2;
}
struct segtree{
int n;
vec(N) seg;
segtree(int _n=0){
init(_n);
}
void init(int _n){
n=_n;
seg.resize(n*4);
}
N merge(N l,N r){
if(!sz(l.fr)){
return r;
}else if(!sz(r.fr)){
return l;
}
N res;
res.val=l.val+r.val;
res.len=l.len+r.len;
vec(pii) leftover;
//from back to front
rep(i,sz(l.bk)){
//gcd
int g=l.bk[i].se;
if(g==1) continue;
//suffix sum in l node
int now=0;
per(j,i+1){
now+=l.bk[j].fi;
}
bool pok=0;
rep(j,sz(r.fr)){
g=gcd(g,r.fr[j].se);
if(g==1){
pok=1;
res.val+=f(now,l.bk[i].fi);
break;
}
now+=r.fr[j].fi;
}
if(!pok){
leftover.pb(l.bk[i]);
}
}
res.bk=r.bk;
//from leftover should be pushed in res.bk
if(sz(leftover)){
int g=0;
rep(i,sz(r.bk)){
g=gcd(g,r.bk[i].se);
}
vec(pii) rbts=res.bk;
rep(i,sz(leftover)){
g=gcd(g,leftover[i].se);
assert(g!=-1);
if(g==rbts.back().se){
rbts.back().fi+=leftover[i].fi;
}else{
rbts.pb(pii(leftover[i].fi,g));
}
}
res.bk=rbts;
}
res.fr=l.fr;
//merge front of l node with r.bk
{
int now=0,g=0;
rep(i,sz(l.fr)){
now+=l.fr[i].fi;
g=gcd(g,l.fr[i].se);
}
if(now==l.len and g!=1){
rep(i,sz(r.fr)){
g=gcd(g,r.fr[i].se);
if(g==res.fr.back().se){
res.fr.back().fi+=r.fr[i].fi;
}else{
res.fr.pb(pii(r.fr[i].fi,g));
}
if(g==1) break;
}
}
}
return res;
}
void set(int node,int l,int r,int pos,int v){
if(l==r-1){
seg[node].fr.clear();
seg[node].bk.clear();
seg[node]=N(0,1,{{1,v}});
return;
}
int m=(l+r)/2;
if(pos<m){
set(node*2+1,l,m,pos,v);
}else{
set(node*2+2,m,r,pos,v);
}
seg[node]=merge(seg[node*2+1],seg[node*2+2]);
}
void set(int pos,int v){
set(0,0,n,pos,v);
}
N prod(int node,int l,int r,int _l,int _r){
if(l>=_r or r<=_l){
return N();
}
if(_l<=l and r<=_r){
return seg[node];
}
int m=(l+r)/2;
N vl=prod(node*2+1,l,m,_l,_r);
N vr=prod(node*2+2,m,r,_l,_r);
return merge(vl,vr);
}
int prod(int l,int r){
N res=prod(0,0,n,l,r);
int ans=res.val;
int now=0;
for(auto p:res.bk){
if(p.se==1) break;
// print("go",p.se);
now+=p.fi;
ans+=f(now,p.fi);
}
return ans;
}
};
signed main(){
_3xaMC2q;
int n,q;
cin>>n>>q;
vi a(n);
rep(i,n){
cin>>a[i];
}
segtree seg(n);
rep(i,n){
seg.set(i,a[i]);
}
// print(seg.prod(0,n));
rep(i,q){
int t;
cin>>t;
if(t==2){
int l,r;
cin>>l>>r;
l-=1;
print(seg.prod(l,r));
}else{
int id,v;
cin>>id>>v;
id-=1;
seg.set(id,v);
}
}
}
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