1 #include <cstdio>
2 #include <iostream>
3 #include <algorithm>
4 #include <cstring>
5 using namespace std;
6 char s[1000010];
7 int k,n,a[1000010],sum;
8 double x,q,a1,a2,ans;
9 int main()
10 {
11 scanf("%s %d",s,&k);
12 n=strlen(s);
13 for (int i=1;i<=n;i++)
14 {
15 a[i]=s[i-1]-'0';
16 sum+=a[i];
17 }
18 x=1.0; q=(n-1.0)*n/2.0;
19 for (int i=1;i<=k;i++) x=x*(1.0-(n-1.0)/q)+(1.0-x)/q;
20 for (int i=1;i<=n;i++)
21 {
22 a1=i*(double)(n-i+1.0)/(double)(n*(n+1.0)/2.0);
23 a2=(double)a[i]*x+(double)(sum-a[i])/(double)(n-1.0)*(1.0-x);
24 ans+=a1*a2;
25 }
26 printf("%.9lf",ans);
27 return 0;
28 }