For the classic Josephus problem, there exists two classic algorithms.
The algorithm A has time complexity O(lgn) and comes from <discrete mathematics>.
/* Algorithm A */
int solve(int N/*The magic number 1999*/, int m/*length of the text*/)
{
    long long z = 1;
    while (z < (N - 1LL/*int may overflow here*/) * m + 1)
    {
        z = (z * N + N - 2) / (N - 1);
    }
    return m * N - z;
}

The algorithm B is the classic O(n) algorithm.
int solve(int N/*The magic number 1999*/, int m/*length of the text*/)
{
    int z = 0;
    for (int k = 2; k <= m; ++k)
    {
        z = (z + N) % k;
    }
    return z;
}

In my submissions, algorithm A costs 0.015s, and algorithm B costs 0.001s.
Maybe arithmetic operations for "long long" is a little too slow?