+def most_trivial(n, m):
+ """The most trivial possible bound."""
+ return m
+
+def trivial(n, m):
+ """Trivial upper bound of m/2.
+
+If m does not divide n, then at least one m-stick must be cut into
+more than one piece, reducing the best option to at most m/2."""
+ if n % m == 0:
+ return None
+ return Fraction(m, 2)
+