13162

#include <bits/stdc++.h>
using namespace std;
#define PB push_back
#define ZERO (1e-10)
#define INF (1<<29)
#define CL(A,I) (memset(A,I,sizeof(A)))
#define DEB printf("DEB!\n");
#define D(X) cout<<"  "<<#X": "<<X<<endl;
#define EQ(A,B) (A+ZERO>B&&A-ZERO<B)
typedef long long ll;
typedef long double ld;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef pair<int,int> ii;
typedef vector<ii> vii;
#define IN(n) int n;scanf("%d",&n);
#define FOR(i, m, n) for (int i(m); i < n; i++)
#define REP(i, n) FOR(i, 0, n)
#define F(n) REP(i, n)
#define FF(n) REP(j, n)
#define FT(m, n) FOR(k, m, n)
#define aa first
#define bb second
void ga(int N,int *A){F(N)scanf("%d",A+i);}
#define MX (60)
#define DP (666)
ll pt[MX][MX];
void PT(){
    F(MX){
        pt[i][0]=pt[i][i]=1;
        FT(1,i)pt[i][k]=pt[i-1][k]+pt[i-1][k-1];
    }
}
set<int> S;
bool   cn[11][11][11][DP];
double dp[11][11][11][DP];
int N,T,C,A,B,a;
double dyn(int,int,int,int);
double fm(int M,int K){return pt[M][K];}
double rec(int A,int B,int C,int D,int R,int u,int r){
    int t;
    double S=0;
    if(!u){
        t=min(A,r)+1;
        F(t)S+=fm(A,i)*rec(A-i,B,C,D,R,u+1,r-i);
    }if(u==1){
        t=min(B,r)+1;
        F(t)S+=fm(B,i)*rec(A,B-i,C,D,R,u+1,r-i);
    }if(u==2){
        t=min(C,r)+1;
        F(t)S+=fm(C,i)*rec(A,B,C-i,D,R,u+1,r-i);
    }if(u==3){
        if(r>R)return 0;
        S=dyn(A,B,C,D)*pt[R][r]/pt[N][T];
    }
    return S;
}
double dyn(int A,int B,int C,int D){
    if(!C&(!A|!B))return 0;
    if(D==DP)return 0;
    double&v=dp[A][B][C][D];
    if(cn[A][B][C][D]++)return v;
    return v=rec(A,B,C,D+1,N-A-B-C,0,T)+1;
}
int main(void){
    PT();
    while(~scanf("%d%d%d",&N,&T,&C)){
        S.clear(),A=B=C,CL(cn,0);
        F(C)scanf("%d",&a),S.insert(a);
        F(C){
            scanf("%d",&a);
            if(S.count(a))--A,--B;
        }
        printf("%.12lf\n",dyn(A,B,C-A,0));
    }
    return 0;
}