Problem p02781 (python)

Fixed submission:
def run():
  N = list(map(int, list(input())))
  K = int(input())
  Nlen = len(N)
  dp = [[[0]*(K+2) for _ in range(2)] for n in range(Nlen+1)]
  dp[0][0][0] = 1
  for nlen in range(Nlen):
    dN = N[nlen]
    for d in range(10):
      for j in range(2):
        for k in range(K+2):
          flagj = j or d < dN
          if (flagj == 0) and (d > dN): continue
          flagk = min(K+1, k+(d != 0))
          dp[nlen+1][flagj][flagk] += dp[nlen][j][k]
  print(dp[-1][0][K]+dp[-1][1][K])
  
if __name__ == '__main__':
    run()

Buggy submission (verdict: Runtime Error):
from operator import mul
from functools import reduce

def com(n,r):
    r = min(n-r,r)
    if r == 0: return 1
    over = reduce(mul, range(n, n - r, -1))
    under = reduce(mul, range(1,r + 1))
    return over // under

def run():
  N = int(input())
  K = int(input())
  Nnum = len(str(N))
  #1
  all1 = com(Nnum, K)*9**K
  #2
  all2 = (9-int(str(N)[0]))*com(Nnum-1, K-1)*9**(K-1)
  if K == 1:
    print(all1-all2)
  #3
  elif K == 2:
    all3 = 0
    for n in range(1, Nnum):
      N2 = int(str(N)[n])
      if N2 != 0:
        all3 += 9-N2
        break
      all3 += 9
    else:
      all3 = (Nnum-1)*9
    print(all1-all2-all3)
  #4
  else:
    all3 = 0
    count = 0
    for n in range(1, Nnum):
      N2 = int(str(N)[n])
      if N2 != 0:
        if count == 0:
          all3 += (9-N2)*com(Nnum-n-1, 1)*9
        elif count == 1:
          all3 += 9-N2
        count += 1
        if count == 2:
          break
      elif count == 0:
        all3 += 9*(Nnum-n-1)*9
      else:
        all3 += 9
    else:
      if count == 0:
        all3 = com(Nnum-1, 2)*9*9
      else:
        all3 = (Nnum-1)*9
    print(all1-all2-all3)
    
  

if __name__ == '__main__':
    run()

Buggy submission (verdict: Runtime Error):
from operator import mul
from functools import reduce

def com(n,r):
    r = min(n-r,r)
    if r == 0: return 1
    over = reduce(mul, range(n, n - r, -1))
    under = reduce(mul, range(1,r + 1))
    return over // under

def run():
  N = int(input())
  K = int(input())
  Nnum = len(str(N))
  #1
  all1 = com(Nnum, K)*9**K
  #2
  all2 = (9-int(str(N)[0]))*com(Nnum-1, K-1)*9**(K-1)
  if K == 1:
    print(all1-all2)
  #3
  elif K == 2:
    all3 = 0
    for n in range(1, Nnum):
      N2 = int(str(N)[n])
      if N2 != 0:
        all3 += 9-N2
        break
      all3 += 9
    else:
      all3 = (Nnum-1)*9
    print(all1-all2-all3)
  #4
  else:
    all3 = 0
    count = 0
    for n in range(1, Nnum):
      N2 = int(str(N)[n])
      if N2 != 0:
        if count == 0:
          all3 += (9-N2)*com(Nnum-n-1, 1)*9
        elif count == 1:
          all3 += 9-N2
        count += 1
        if count == 2:
          break
      elif count == 0:
        all3 += 9*(Nnum-n-1)*9
      else:
        all3 += 9
    else:
      if count == 0:
        all3 = com(Nnum-1, 2)*9*9
      else
        all3 = (Nnum-1)*9
    print(all1-all2-all3)
    
  

if __name__ == '__main__':
    run()

Buggy submission (verdict: Runtime Error):
from operator import mul
from functools import reduce

def com(n,r):
    r = min(n-r,r)
    if r == 0: return 1
    over = reduce(mul, range(n, n - r, -1))
    under = reduce(mul, range(1,r + 1))
    return over // under

def run():
  N = int(input())
  K = int(input())
  Nnum = len(str(N))
  #1
  all1 = com(Nnum, K)*9**K
  #2
  all2 = (9-int(str(N)[0]))*com(Nnum-1, K-1)*9**(K-1)
  if K == 1:
    print(all1-all2)
  #3
  elif K == 2:
    all3 = 0
    for n in range(1, Nnum):
      N2 = int(str(N)[n])
      if N2 != 0:
        all3 += 9-N2
        break
      all3 += 9
    else:
      all3 = (Nnum-1)*9
    print(all1-all2-all3)
  #4
  else:
    all3 = 0
    count = 0
    for n in range(1, Nnum):
      N2 = int(str(N)[n])
      if N2 != 0:
        if count == 0:
          all3 += (9-N2)*com(Nnum-n-1, 1)*9
        elif count == 1:
          all3 += 9-N2
        count += 1
        if count == 2:
          break
      elif count == 0:
        all3 += 9*(Nnum-n-1)*9
      else:
        all3 += 9
    else:
      all3 = (Nnum-1)*9
    print(all1-all2-all3)
    
  

if __name__ == '__main__':
    run()