#pragma optimize("-O2")
#include<bits/stdc++.h>
#define sight(c) ('0'<=c&&c<='9')
#define LL unsigned long long
#define N 100009
#define db long double
const LL mo=(1<<25)-1;
using namespace std;
struct NL{LL a,b;NL() {a=b=0;}NL(LL x,LL y):a(x),b(y){}inline NL operator ^(const NL &A)const &{return NL(A.a^a,A.b^b);}inline NL operator ^(const LL &A)const &{return NL(a,A^b);}inline NL operator +(const NL &A)const &{NL T;T.a=A.a+a; T.b=A.b+b;if (T.b>mo) T.a+=T.b>>25,T.b&=mo;return T;}inline NL operator +(const LL &A)const &{NL T; T.a=a; T.b=A+b;if (T.b>mo) T.a+=T.b>>25,T.b&=mo;return T;}inline NL operator *(const NL &A)const &{NL T;T.a=(A.a*a<<25)+A.a*b+A.b*a; T.b=A.b*b;if (T.b>mo) T.a+=T.b>>25,T.b&=mo;return T;}inline NL operator *(const LL &A)const &{NL T;T.a=a*A; T.b=A*b;if (T.b>mo) T.a+=T.b>>25,T.b&=mo;return T;}inline LL ok(int x){LL T=b&(1ll<<x)-1;b>>=x; b|=(a&(1ll<<x)-1)<<(25-x);a>>=x;return T;}
};
inline void read(LL &x){static char c;for (c=getchar();!sight(c);c=getchar());for (x=0;sight(c);c=getchar()) x=x*10+c-48;
}
void write(LL x) {if (x<10) { putchar('0'+x); return;} write(x/10); putchar('0'+x%10);
}
inline void writeln(LL x) {if (x<0) putchar('-'),x*=-1; write(x); putchar('\n');
}
LL n,k,ans,X,A[N],P[65],r,OT[65],O;
NL Ans;
void Guass()
{for (int i=1;i<=n;i++)for (int j=62;~j;j--)if ((A[i]>>j)&1) if (!P[j]) {P[j]=A[i]; break;} else A[i]^=P[j];for (int j=0;j<=62;j++) if (P[j]) OT[r++]=P[j];
}
int b[79];
inline NL pow(NL x,int k){NL anw=NL(0,1);for (;k;k>>=1,x=x*x)if (k&1) anw=anw*x;return anw;
}
void dfs(NL x,int t){if (!(t^r)) { Ans=Ans+pow(x,k); return;} dfs(x^OT[t],t+1);  dfs(x,t+1);
}
int main () {    freopen("malygos.in","r",stdin);freopen("malygos.out","w",stdout);read(n); read(k);for (int i=1;i<=n;i++) {read(A[i]); for (int j=0;j<=63;j++) b[j]|=(A[i]>>j)&1;}if (k==1) {for (int j=63;~j;j--) if (b[j]) ans+=1ll<<j; write(ans>>1); if (ans&1) puts(".5\n"); return 0;}if (k==2) {for (int j=31;~j;j--) if (b[j]) Ans=Ans+(1ull<<2*j+1);for (int i=31;~i;i--) {for (int j=0;j<i;j++) {int c[4]={};for (int k=1;k<=n;k++)  c[(A[k]>>i&1)<<1|(A[k]>>j&1)]=1;for (int k=0;k<4;k++) for (int ii=0;ii<4;ii++) for (int jj=0;jj<4;jj++) if (c[ii]&&c[jj])  c[ii^jj] = 1;int s=0;for (int k=0;k<4;k++) s+=c[k];if (c[3])     Ans=Ans+((LL)(8/s)*(1ULL<<i+j));}}LL g=Ans.ok(2);LL T=(Ans.a<<25)+Ans.b;write(T);LL MM=1<<2;if (g) {putchar('.');while (g) {g*=10; putchar('0'+g/MM); g%=MM;}}return 0;}Guass();dfs(NL(0,0),0);LL g=Ans.ok(r);LL T=(Ans.a<<25)+Ans.b;write(T);LL MM=1<<r;if (g) {putchar('.');while (g) {g*=10; putchar('0'+g/MM); g%=MM;}}return 0;
}