#include <bits/stdc++.h>

using namespace std;
typedef long long ll;

const int N = 1e5 + 3, MOD = 998244353;//1e9 + 7;

int32_t main() {

    cin.tie(0);cin.sync_with_stdio(0);
    cout.tie(0);cout.sync_with_stdio(0);

    int n ,m;
    cin >> n >> m;

    double s[n] , d[m] ;

    for (int i = 0; i < n - 1; ++i) {
        cin >> s[i] ;
    }

    for (int i = 0; i < m; ++i) {
        cin >> d[i] ;
    }

    char a[n][m] ;

    for (int i = 0; i < n; ++i) {

        for (int j = 0; j < m; ++j) {
            cin >> a[i][j] ;
        }
    }

    int c =0 ;
    for(int j =0 ; j < m ; j++) c+= (a[n-1][j] == 'X');

    double ans = 1;

    for(int i =0 ; i < n-1; i++)
    {
        double dp[m+1][m+1] ;

        memset(dp , 0 ,sizeof dp);

        int be = 0;
        for (int j = 0; j < m; ++j) {
            be += (a[i][j] == 'X') ;
        }

        for(int cc = 0 ; cc <= c-be; cc++) dp[m][cc] =1;

        for(int j = m-1 ; j >= 0 ; j--)
        {
            for(int cc = 0; cc <= c - be ; cc++)
            {
                double & ret = dp[j][cc] ;

                if(a[i][j] != '?')
                {
                    ret = dp[j+1][cc] ;
                    continue;
                }

                ret = (1 - s[i]*d[j])* dp[j+1][cc] ;

                ret += s[i]*d[j]*dp[j+1][cc+1] ;
            }
        }

        ans *= dp[0][0];
    }

    cout << fixed << setprecision(11) << ans ;

    return 0;
}