#include<bits/stdc++.h>

#define ll long long
#define pp push_back
#define endl '\n'
#define all(x) x.begin(),x.end()
#define ld long double
#define PI acos(-1)
#define sin(a) sin((a)*PI/180)
#define cos(a) cos((a)*PI/180)
#define ones(x) __builtin_popcountll(x)
//#define int ll

using namespace std;

void Drakon() {
    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
}

unsigned long long inf = 1e10;
const double EPS = 1e-6;
const int MOD = 1000000007, N = 105, LOG = 25;

ll gcd(ll x, ll y) {
    return y ? gcd(y, x % y) : x;
}

ll lcm(ll a, ll b) {
    return (a * b) / __gcd(a, b);
}

ll mul(const ll &a, const ll &b) {
    return (a % MOD + MOD) * (b % MOD + MOD) % MOD;
}

ll add(const ll &a, const ll &b) {
    return (a + b + 2 * MOD) % MOD;
}

ll pw(ll x, ll y) {
    ll ret = 1;
    while (y > 0) {
        if (y % 2 == 0) {
            x = mul(x, x);
            y = y / 2;
        } else {
            ret = mul(ret, x);
            y = y - 1;
        }
    }
    return ret;
}

int t, p;
vector<double>s, d;
vector<char> state[N];
bool vis[N][N][N];
double dp[N][N][N];

double slv(int i, int rem, int team){
    if(rem < 0)return 0;
    if(i == p){
        return (rem == 0);
    }
    double &ret = dp[i][rem][team];
    if(vis[i][rem][team])return ret;
    vis[i][rem][team] = true;

    if(state[team][i] == '?'){
        ret = slv(i + 1, rem, team) * (1 - s[team] * d[i]) + slv(i + 1, rem - 1, team) * s[team] * d[i];
    }
    else if(state[team][i] == '-'){
        ret = slv(i + 1, rem, team);
    }
    else{
        ret = slv(i + 1, rem - 1, team);
    }

    return ret;
}

void solve() {
    cin >> t >> p;
    s.resize(t);
    d.resize(p);
    for (int i = 0; i < t - 1; ++i) {
        cin >> s[i];
    }
    for (int i = 0; i < p; ++i) {
        cin >> d[i];
    }

    int cnt = 0;
    for (int i = 0; i < t; ++i) {
        state[i].resize(p);
        for (int j = 0; j < p; ++j) {
            cin >> state[i][j];
            if(i == t - 1)cnt += state[i][j] == 'X';
        }
    }

    double ans = 1;
    for (int i = 0; i < t - 1; ++i) {
        double tmp = 0;
        for (int j = 0; j <= cnt; ++j) {
            tmp += slv(0, j, i);
        }
        ans *= tmp;
    }
    cout << fixed << setprecision(10) << ans;
}

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