#include <bits/stdc++.h>
#define pb push_back
#define F first
#define S second
#define all(v) v.begin(),v.end()
#define Gondozu ios::sync_with_stdio(false);cout.tie(NULL);cin.tie(NULL);

using namespace std;
using ll = long long;
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;

double dp[N][N], d[N], s[N], prob[N];
int vis[N][N], vid, t, p, solved;
char a[N][N];

double slv(int j, int cnt, int i){
    if(j == p)
        return cnt > solved;
    double &ret = dp[j][cnt];
    if(vis[j][cnt] == vid)
        return ret;
    vis[j][cnt] = vid;

    ret = 0;
    if(a[i][j] == '?')
        ret = (1 - s[i]*d[j]) * slv(j+1,cnt,i) + s[i]*d[j] * slv(j+1,cnt+1,i);
    else
        ret = slv(j+1, cnt+(a[i][j]=='X'), i);

    return ret;
}

double dp2[N][N];
bool vis2[N][N];
double slv2(int i, int cnt){
    if(i == t-1)
        return cnt > 0;
    double &ret = dp2[i][cnt];
    if(vis2[i][cnt])
        return ret;
    vis2[i][cnt] = true;

    ret = prob[i]*slv2(i+1,cnt+1) + (1-prob[i])*slv2(i+1,cnt);

    return ret;
}

void TC()
{
    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 >> a[i][j];
            if(i == t-1) solved += a[i][j] == 'X';
        }
    }

    for (int i = 0; i < t-1; ++i) {
        ++vid;
        prob[i] = slv(0,0,i);
    }

    cout << fixed << setprecision(7) << 1-slv2(0,0);
}

int32_t main() {
#ifndef ONLINE_JUDGE
    freopen("input.in", "r", stdin); freopen("output.out", "w", stdout);
#endif
    Gondozu
    TC();
    return 0;
}