There are m different colors of beads. Define a necklace of length n is a cyclic string that successively connects n beads, taking all rotations and overturnings as equivalent.
For example, [1, 2, 3, 4] is equivalent to [2, 3, 4, 1], [3, 4, 1, 2] and [4, 1, 2, 3] (by ro-tation); and [1, 2, 3, 4] is equivalent to [1, 4, 3, 2], [3, 2, 1, 4], [2, 1, 4, 3] and [4, 3, 2, 1] (by overturning).
Moreover, each time you could transpose the beads of color i to color (i mod m) + 1 for all i at the same time.
After some operations, if a necklace A becomes B, then B is equivalent to A.
Count the number of necklaces modulo 998244353.