HELP | DP | Atcoder | Recursive top Down

help
, ,
1

hey, i tried to solve this_problem of Atcoder using top_down approach,but it shows TLE for two sub-tasks>
am i missing any edge case or it just because of recursion .
one thing to mention :slightly_smiling_face: that i know to solve the problem iteratively (bottom up) but curious to know why my recursive method failed.

submission_link
code for quick review.

import sys 
sys.setrecursionlimit(10**6)
def dp(n,k,cache,height):
  #print(cache)
  if n==0:
    return 0
  elif n in cache :
    return cache[n]
  else:
    lcl_min=float('inf')
    i=1
    while n-i>=0 and i<=k:
      lcl_min=min(lcl_min,dp(n-i,k,cache,height)+abs(height[n]-height[n-i]))
      i+=1
      
    cache[n]=lcl_min  
    return cache[n]
n,k=map(int,input().split())
h=list(map(int,input().split()))
print(dp(n-1,k,dict(),h))

thanks a ton in advance…