How to assign -1 to size_type?

I'm writing a function to partition a vector according to a predicate.
For example:

vector<string>::size_type partition(vector<Student_info> &v)
{
	vector<string>::size_type i, j;
	i = -1;
	j = v.size();

	while (true)
	{
		cout << i << ' ' << j << endl;
		do ++i; while (i <= v.size() - 1 && !fgrade(v[i]));
		do --j; while (j >= 0 && fgrade(v[j]));
		if (i > j)
			break;
		exchange(v, i, j);
	}
	return i;
}
fgrade will return true if the student's grade is less than 60.

I want the i is the position one before the first element
and j is the position one after the last element.
But size_type is an unsigned int, so it's wrong to assign -1 to i, i
will become a larger integer.
If I change type of i and j to int, I'll encounter signed/unsigned
mismatch problem.

What can I do to handle this situation?