Simplify the recurrence

for dp[n][1] : count of *ALL* paths without the consideration of
the "D" limitation. Because some predecessors have already satisified
the requirement.
  1. dp[0][1] = 1
  2. dp[n][1] = sum(dp[n - i][1]), 1 <= i <= K, and 0 <= (n - i)

for dp[n][1] : count of paths with the consideration of the "D"
limitation.
  1. dp[0][0] = 0
  2. dp[n][0] = sum(dp[n - i][(i >= D)]), 1 <= i <= K, and 0 <= (n - i)

if the weight "i" of edge is already large or equal to D,
then we can simply consider all possible paths of the sub-tree below the edge