output_description: Print the possible ways Ringo could have thrown in K balls, modulo 998244353.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N K
attempt: m = 998244353
  
  
  def c(n, r):
      return (g[n] * h[r] * h[n - r]) % m
  
  
  g = [1, 1]
  h = g[:]
  v = [0, 1]
  for i in range(2, 999999):
      g.append((g[-1] * i) % m)
      v.append((-v[m % i] * (m // i)) % m)
      h.append((h[-1] * v[i]) % m)
  N, K = map(int, input().split())
  P = 0
  for k in range(N - 1, K):
      P += c(K - 1, k)
  print(P)
  
problem_description: Statement
  
  In Republic of AtCoder, Snuke Chameleons (Family: Chamaeleonidae, Genus:
  Bartaberia) are very popular pets. Ringo keeps N Snuke Chameleons in a cage.
  
  A Snuke Chameleon that has not eaten anything is blue. It changes its color
  according to the following rules:
  
    * A Snuke Chameleon that is blue will change its color to red when the number of red balls it has eaten becomes strictly larger than the number of blue balls it has eaten.
    * A Snuke Chameleon that is red will change its color to blue when the number of blue balls it has eaten becomes strictly larger than the number of red balls it has eaten.
  
  Initially, every Snuke Chameleon had not eaten anything. Ringo fed them by
  repeating the following process K times:
  
    * Grab either a red ball or a blue ball.
    * Throw that ball into the cage. Then, one of the chameleons eats it.
  
  After Ringo threw in K balls, all the chameleons were red. We are interested
  in the possible ways Ringo could have thrown in K balls. How many such ways
  are there? Find the count modulo 998244353. Here, two ways to throw in balls
  are considered different when there exists i such that the color of the ball
  that are thrown in the i-th throw is different.
samples: [{"input": "2 4", "output": "7\n    \n\nWe will use `R` to represent a red ball, and `B` to represent a blue ball.\nThere are seven ways to throw in balls that satisfy the condition: `BRRR`,\n`RBRB`, `RBRR`, `RRBB`, `RRBR`, `RRRB` and `RRRR`.\n\n* * *"}, {"input": "3 7", "output": "57\n    \n\n* * *"}, {"input": "8 3", "output": "0\n    \n\n* * *"}, {"input": "8 10", "output": "46\n    \n\n* * *"}, {"input": "123456 234567", "output": "857617983"}]