int hugs(const string& members, const string& fans)
{
    int N = members.size(), M = fans.size();
    vector<int> A(N), B(M);
    for (int i = 0; i < N; ++i) A[i] = (members[i] == 'M');
    for (int i = 0; i < M; ++i) B[M - i - 1] = (fans[i] == 'M');
    //karatsuba 알고리즘에서 자리 올림은 생략한다.
    vector<int> C = karatsuba(A, B);
    int allHugs = 0;
    for (int i = N - 1; i < M; ++i)
        if (C[i] == 0)
            ++allHugs;
    return allHugs;
}

vector<int > multiply(const vector<int>& a, const vector<int>& b)
{
    vector<int> c(a.size() + b.size() + 1, 0);
    for (int i = 0; i < a.size(); ++i)
        for (int j = 0; j < b.size(); ++j)
            c[i + j] += a[i] * b[j];
    normalize(c)
    return c;
}