#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <cmath>
#include <vector>
#include <set>
#include <map>
#include <stack>
#include <unordered_set>
#include <unordered_map>
#include <queue>
#include <ctime>
#include <cassert>
#include <complex>
#include <string>
#include <cstring>
#include <chrono>
#include <random>
#include <bitset>
#include <array>
#include <climits>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <cmath>
#include <vector>
#include <set>
#include <map>
#include <stack>
#include <unordered_set>
#include <unordered_map>
#include <queue>
#include <ctime>
#include <cassert>
#include <complex>
#include <string>
#include <cstring>
#include <chrono>
#include <random>
#include <bitset>
#include <array>
#include <climits>

// #pragma GCC optimize("O3")
// #pragma GCC optimize ("unroll-loops")
// #pragma GCC target("avx,avx2,fma")

using namespace std;

#define ll long long
#define ld long double

const int N = 100 + 5, lg = 19, mod = 998244353;
const int M = 1e7 + 5;
const int INF = 1e9;

int t, p, problems;
ld s[N], d[N], dp[N][N], ans = 1.0l;
bool vis[N][N][N];
char c[N][N];

ld solve(int team, int idx, int cnt) {
    if (idx == p) {
        return cnt <= problems;
    }
    auto &ret = dp[idx][cnt];
    if (vis[team][idx][cnt]) {
        return ret;
    }
    vis[team][idx][cnt] = true;
    ld prob_solve;
    if (c[team][idx] == 'X') {
        prob_solve = 1.0l;
    } else if (c[team][idx] == '-') {
        prob_solve = 0.0l;
    } else {
        prob_solve = s[team] * d[idx];
    }
    ld prob_skip = 1.0l - prob_solve;
    ret = prob_skip * solve(team, idx + 1, cnt);
    ret += prob_solve * solve(team, idx + 1, cnt + 1);
    return ret;
}

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cin >> t >> p;
    for (int i = 0; i < t - 1; ++i) {
        cin >> s[i];
    }
    for (int i = 0; i < p; ++i) {
        cin >> d[i];
    }
    for (int i = 0; i < t; ++i) {
        for (int j = 0; j < p; ++j) {
            cin >> c[i][j];
        }
    }
    for (int i = 0; i < p; ++i) {
        problems += (c[t - 1][i] == 'X');
    }
    for (int i = 0; i < t - 1; ++i) {
        ans *= solve(i, 0, 0);
    }
    cout << fixed << setprecision(10) << ans << '\n';
    return 0;
}