int eval(config v) {
int sum;
int E{0};
sum = accumulate(all(v),0);
if (sum == 1) {
if (v.back()==1) return 1;
E = 1;
}
for (size_t i = 0; i < v.size(); i++) {
if (v[i] == 0) continue;
config w{v};
w[i]--;
for (size_t j = i+1; j < w.size(); j++) w[j]++;
int prob = (int) v[i] * inverse(sum);
E = add(E, mult(eval(w), prob));
}
return E;
}
void visit(const config& v) {
for (size_t i=0;i<v.size()-1;i++) cout << v[i] << ' ';
cout << v.back() << ": " << eval(v) << endl;
}