#include<algorithm>

 #include<cstdio>

 #include<cmath>

 #include<cstring>

 #include<iostream>

 int block,n,m;

 int s[][],a[];

 const double eps=1e-;

 int read(){

     int t=,f=;char ch=getchar();

     while (ch<''||ch>''){if (ch=='-') f=-;ch=getchar();}

     while (''<=ch&&ch<=''){t=t*+ch-'';ch=getchar();}

     return t*f;

 }

 void init(){

     n=read();m=read();

     for (int i=;i<=n;i++) a[i]=read();

     block=ceil(sqrt(n))+0.1;

     for (int i=;i<=block;i++)

      for (int j=;j<=i;j++)

       for (int k=j;k<=n;k+=i)

        s[i][j]+=a[k];

 }

 void modify(int x,int y){

     int T=y-a[x];

     for (int i=;i<=block;i++)

       s[i][(x-)%i+]+=T;

     a[x]=y;

 }

 double deal(int k,int d){

     if (d<=block) return s[d][(k-)%d+];

     double res=;

     for (int i=(k-)%d+;i<=n;i+=d)

      res+=(double)a[i];

     return res;

 }

 void solve(){

     while (m--){

         int opt=read();

         if (opt==){

             int x=read(),y=read();

             modify(x,y);continue;

         }

         int num=0x7fffffff,t,k,d;

         t=read();k=read();d=read();for (int i=;i<=t;i++){int l=read();num=std::min(num,l);}

         if (t==) {printf("%.4f\n",deal(k,d));continue;}

         double ans=(double)a[k],p=;

         int N=num;

         for (int i=k+d,Num=n-;i<=n&&num>;i+=d,Num--,num--){

             p=p*num/Num;ans+=p*a[i];

             if (p<eps&&n>=) break;

         }

         num=N;p=;

         for (int i=k-d,Num=n-;i>=&&num>;i-=d,Num--,num--){

             p=p*num/Num;ans+=p*a[i];

             if (p<eps&&n>=) break;

         }

         printf("%.4f\n",ans);

     }

 }

 int main(){

     init();

     solve();

 }