#include <bits/stdc++.h>

typedef long double ld;
typedef long long ll;
using namespace std;
int di[] = {1, 0, -1, 0, 0, 1, -1, 1};
int dj[] = {0, 1, 0, -1, -1, 0, 1, -1};

const ll oo = 1e18;
const int N = 2e5 + 5, M = 1e5 + 5, MOD = 998244353;
#define EPS 1e-9

int n, m, cnt[105], vis[105][105];
double dp[105][105], team[105], problem[105];
char c[105][105];

double solve(int id, int idx, int rem) {
    if (rem < 0) return 0;
    if (idx > m) return 1;
    double &ret = dp[idx][rem];
    if (vis[idx][rem] == id) return ret;
    vis[idx][rem] = id;
    if (c[id][idx] != '?') return ret = solve(id, idx + 1, rem);
    double prob = team[id] * problem[idx];
    ret = prob * solve(id, idx + 1, rem - 1) + (1.0 - prob) * solve(id, idx + 1, rem);
    return ret;
}

int main() {
    //  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
    cin >> n >> m;
    for (int i = 1; i < n; i++) cin >> team[i];
    for (int i = 1; i <= m; i++) cin >> problem[i];
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= m; j++) {
            cin >> c[i][j];
            if (c[i][j] == 'X') cnt[i]++;
        }
    }
    double ans = 1;
    for (int i = 1; i < n; i++) ans *= solve(i, 1, cnt[n] - cnt[i]);
    cout << fixed << setprecision(8) << ans;
    return 0;
}