Round 1, count 1 space starting from position 0:        _ 1 _ _ _
Round 2, count 2 spaces starting from position 1:       _ 1 _ _ 2
Round 3, count 3 spaces starting from position 2:       3 1 _ _ 2
Round 4, count 4 spaces starting from position 3:       3 1 4 _ 2
Round 5, count 5 spaces starting from position 4:       3 1 4 5 2

memset( ans, 255, sizeof(ans) );
while ( cur <= n )
{
    int i, cnt;
    int left = n - cur + 1; // count how many spaces left
    left = cur % left + 1; // this line is critical, mod to save time!

    for ( i = pos, cnt = 0; ; ++i ) // simulate the process
    {
        if ( i > n ) i = 1;
        if ( ans[i] == -1 ) ++cnt;
        if ( cnt == left ) break;
    }

    ans[i] = cur;
    pos = i;

    ++cur;
}