#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;

#define fi first
#define se second
#define pp push_back
#define all(x) (x).begin(), (x).end()
#define Ones(n) __builtin_popcount(n)
#define endl '\n'
#define mem(arrr, xx) memset(arrr,xx,sizeof arrr)
//#define int long long
#define debug(x) cout << (#x) << " = " << x << endl

void Gamal() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
#ifdef Clion
    freopen("input.txt", "r", stdin), freopen("output.txt", "w", stdout);
#endif
}

int dx[] = {+0, +0, -1, +1, +1, +1, -1, -1};
int dy[] = {-1, +1, +0, +0, +1, -1, +1, -1};

const double EPS = 1e-9;
const ll OO = 0X3F3F3F3F3F3F3F3F;
const int N = 100 + 5, INF = INT_MAX, MOD = 1e9 + 7, LOG = 20;

int p, vis[N][N], vid;
ld dp[N][N];
vector<ld> cur;

ld slv(int i, int rem) {
    if (rem < 0)return 0;
    if (i == cur.size())return 1;
    ld &ret = dp[i][rem];
    if (vis[i][rem] == vid)
        return ret;
    vis[i][rem] = vid;
    ret = (1 - cur[i]) * slv(i + 1, rem) + cur[i] * slv(i + 1, rem - 1);
    return ret;
}

void solve() {
    int t;
    cin >> t >> p;
    t--;
    vector<ld> v(t);
    for (int i = 0; i < t; ++i) {
        cin >> v[i];
    }
    vector<ld> d(p);
    for (int i = 0; i < p; ++i) {
        cin >> d[i];
    }
    vector<vector<ld>> prob(t);
    vector<int> solved(t);
    for (int i = 0; i < t; ++i) {
        for (int j = 0; j < p; ++j) {
            char c;
            cin >> c;
            if (c == 'X') {
                solved[i]++;
            } else if (c == '?') {
                prob[i].push_back(d[j] * v[i]);
            }
        }
    }
    int cnt = 0;
    for (int i = 0; i < p; ++i) {
        char c;
        cin >> c;
        cnt += c == 'X';
    }

    ld ans = 1;
    for (int i = 0; i < t; ++i) {
        if (solved[i] > cnt) {
            ans = 0;
            break;
        }
        cur = prob[i];
        vid++;
        ans *= slv(0, cnt - solved[i]);
    }
    cout << fixed << setprecision(7) << ans;
}


signed main() {
    Gamal();
    int t = 1;
//    cin >> t;
    while (t--) {
        solve();
    }
}