#include <bits/stdc++.h>

#define pb push_back
#define F first
#define S second
#define MP make_pair
#define all(x) x.begin(),x.end()
#define Hagry ios::sync_with_stdio(false);cout.tie(NULL);cin.tie(NULL);

using namespace std;
using ll = long long;
using ld = long double;
using pi = pair<int, int>;
using vi = vector<int>;
using vpi = vector<pair<int, int>>;
using vvi = vector<vector<int>>;

const int OO = 1e9 + 5;
const int N = 100 + 5;
char board[N][N];
int cnt[N], t, p;
ld dp[N][N][N], s[N], d[N];
bool vis[N][N][N];
int vid;

ld solve(int i, int rem, int team) {
    if (rem == 0)
        return 1;
    if (i == p)
        return 0;

    ld &ret = dp[i][rem][team];
    if (vis[i][rem][team] == vid)
        return ret;
    vis[i][rem][team] = vid;

    if (board[team][i] == 'X')
        ret = solve(i + 1, rem - 1, team);
    else if (board[team][i] == '-')
        ret = solve(i + 1, rem, team);
    else{
        ld get = s[team] * d[i];
        ret = get * solve(i+1, rem-1, team);
        ret += (1.0 - get) * solve(i+1, rem, team);
    }
    return ret;
}

void TC() {
    ++vid;
    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 >> board[i][j];
            cnt[i] += board[i][j] == 'X';
        }
    }

    ld ans = 1;
    for (int i = 0; i < t - 1; ++i) {
        ans *= (ld)1.0 - solve(0,cnt[t-1]+1, i);
    }

    cout << fixed << setprecision(9) << ans;
}

int32_t main() {
#ifndef ONLINE_JUDGE
    freopen("input.in", "r", stdin);
    freopen("output.out", "w", stdout);
#endif
    Hagry
    int tt = 1;
//    cin >> tt;
    while (tt--) {
        TC();
        cout << '\n';
    }
    return 0;
}