#include<iostream>
#include <bits/stdc++.h>

#define ll long long
#define ld long double
#define IO ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
using namespace std;
const int N = 100 + 5, inf = 2e9;
ld dp[N][N];
int vis[N][N], tc;
ld d[N], s[N];
int cnt[N];

ld solve(int player, int i, int rem, vector<int> &problems) {
    if (rem <= 0)return 0;
    if (i == problems.size()) {
        return 1;
    }
    ld &ans = dp[i][rem];
    if (vis[i][rem] == tc)return ans;
    vis[i][rem] = tc;
    ld solvePro = s[player] * d[problems[i]];
    ans = solve(player, i + 1, rem - 1, problems) * solvePro + (1 - solvePro) * solve(player, i + 1, rem, problems);
    return ans;
}

void doWork() {
    int t, p;
    cin >> t >> p;
    for (int i = 0; i + 1 < t; i++) {
        cin >> s[i];
    }
    for (int i = 0; i < p; i++) {
        cin >> d[i];
    }

    ld ans = 1;
    vector<vector<int> > a;

    for (int i = 0; i < t; i++) {
        a.push_back({});
        for (int j = 0; j < p; j++) {
            char c;
            cin >> c;
            if (c == 'X') {
                cnt[i]++;
            } else if (c == '?') {
                a[i].push_back(j);
            }
        }
    }
    for (int i = 0; i + 1 < t; i++) {
        tc++;
        ans *= solve(i, 0, cnt[t - 1] - cnt[i] + 1, a[i]);
    }
    cout << fixed << setprecision(9) << ans;
}

int main() {
    IO
    int t = 1;
    //   cin >> t;
    for (int i = 1; i <= t; i++) {
        //  cout << "Case #" << i << ": ";
        doWork();
    }
}