CF878E Numbers on the blackboard

#include<bits/stdc++.h>
#define Tp template<typename Ty>
#define Ts template<typename Ty,typename... Ar>
#define W while
#define I inline
#define RI register int
#define LL long long
#define Cn const
#define CI Cn int&
#define gc getchar
#define D isdigit(c=gc())
#define pc(c) putchar((c))
using namespace std;
namespace Debug{
    Tp I void _debug(Cn char* f,Ty t){cerr<<f<<'='<<t<<endl;}
    Ts I void _debug(Cn char* f,Ty x,Ar... y){W(*f!=',') cerr<<*f++;cerr<<'='<<x<<",";_debug(f+1,y...);}
    Tp ostream& operator<<(ostream& os,Cn vector<Ty>& V){os<<"[";for(Cn auto& vv:V) os<<vv<<",";os<<"]";return os;}
    #define gdb(...) _debug(#__VA_ARGS__,__VA_ARGS__)
}using namespace Debug;
namespace FastIO{
    Tp I void read(Ty& x){char c;int f=1;x=0;W(!D) f=c^'-'?1:-1;W(x=(x<<3)+(x<<1)+(c&15),D);x*=f;}
    Ts I void read(Ty& x,Ar&... y){read(x),read(y...);}
    Tp I void write(Ty x){x<0&&(pc('-'),x=-x,0),x<10?(pc(x+'0'),0):(write(x/10),pc(x%10+'0'),0);}
    Tp I void writeln(Cn Ty& x){write(x),pc('\n');}
}using namespace FastIO;
Cn int N=1e5+10,p=1e9+7,Inv2=500000004;
Cn LL inf=1e15;
int n,q,a[N],inv[N],pw[N],stk[N],top;
LL s[N],S[N],SS[N],Ans[N];
struct Que{int l,r,id;}Q[N];
vector<int> v[N];
#define pb push_back
int main(){
    RI i,t;for(read(n,q),pw[0]=inv[0]=1,i=1;i<=n;i++) read(a[i]),s[i]=(s[i-1]+1LL*(pw[i]=2LL*pw[i-1]%p)*a[i]%p)%p,inv[i]=1LL*inv[i-1]*Inv2%p;
    for(i=1;i<=q;i++) read(Q[i].l,Q[i].r),Q[i].id=i,v[Q[i].r].pb(i);
    for(i=1;i<=n;i++){
        stk[++top]=i,S[top]=a[i];
        W(top&&S[top]>0) (1LL<<stk[top]-stk[top-1])>(inf-S[top-1])/S[top]?S[top-1]=inf:S[top-1]+=(1<<stk[top]-stk[top-1])*S[top],top--;
        SS[top]=S[top]<inf?(SS[top-1]+S[top])%p:s[i];for(auto j:v[i]){
            stk[top+1]=Q[j].r+1,t=upper_bound(stk+1,stk+top+2,Q[j].l)-stk;
            Ans[Q[j].id]=((2LL*(SS[top]-SS[t-1]+p)%p+1LL*(s[stk[t]-1]-s[Q[j].l-1]+p)*inv[Q[j].l]%p)%p+p)%p;
        }
    }for(i=1;i<=q;i++) writeln(Ans[i]);
    return 0;
}