Necklace with Magic Beads

wkr wants a ring of n magic beads such that:

• There are exactly \( m \) black beads and \( n-m \) white beads.
• No contiguous (cyclic) segment of black beads has length greater than \( k \).

Two rings are considered identical if one can be obtained from the other by a rotation.

Your task is to count the number of distinct valid necklaces (rings) modulo \( 998\,244\,353 \).

Note: When checking the condition on consecutive black beads, consider the beads arranged in a circle (the sequence is cyclic).

inputFormat

The input consists of three integers n, m, and k separated by spaces.

outputFormat

Output a single integer: the number of distinct valid necklaces modulo \( 998\,244\,353 \).

sample

4 2 1

1