Buggy python submission (verdict: Runtime Error):
N=int(input())
K=int(input())
import math
x=math.floor(math.log10(N))+1
def combinations_count(n, r):
  return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
ans=0
if x<K:
  print(0)
  exit(0)
if K==1:
  ans=(x-1)*9
  ans+=(N//10**(x-1))
  print(ans)
elif K==2:
  for i in range(2,x):
    ans+=(9**2)*(i-1)
  f=(N//10**(x-1))
  n=str(N)
  for i in range(1,x):
    if n[i]!='0':
      s_n=x-i
      s=int(n[i])
      break
  ans+=(f-1)*9*(x-1)
  ans+=9*(s_n-1)
  ans+=s
  print(ans)
else:
  for i in range(3,x):
    ans+=(9**3)*combinations_count(i-1,2)
  f=(N//10**(x-1))
  n=str(N)
  s_n=0
  s=0
  t_n=0
  t=0
  for i in range(1,x):
    if n[i]!='0':
      s_n=x-i
      s=int(n[i])
      break
  for i in range(x-s_n+1,x):
    if n[i]!='0':
      t_n=x-i
      t=int(n[i])
      break
  if s_n<=2:
    ans+=(f-1)*9**2*combinations_count(x-1,2)
    if s>0:
      ans+=(s-1)*9*(s_n-1)
    if t_n!=0:
      ans+=9*(t_n-1)
    ans+=t
  else:
    ans+=(f-1)*9**2*combinations_count(x-1,2)
    print(s_n)
    ans+=9**2*combinations_count(s_n-1,2)
    ans+=(s-1)*9*(s_n-1)
    if t_n!=0:
	    ans+=9*(t_n-1)
    ans+=t
  print(ans)

Fixed submission:
Nstr=input()
N=int(Nstr)
K=int(input())
x=len(Nstr)
dp0=[[0]*(K+1) for i in range(x+1)]
dp1=[[0]*(K+1) for i in range(x+1)]

dp1[0][0]=1

for i in range(1,x+1):
  dp0[i][0]=dp0[i-1][0]+dp1[i-1][0]
  for j in range(1,K+1):
    if Nstr[i-1]!='0':
      dp1[i][j]=dp1[i-1][j-1]
      dp0[i][j]+=(dp1[i-1][j-1]*(int(Nstr[i-1])-1)+dp1[i-1][j])
    else:
      dp1[i][j]=dp1[i-1][j]
    dp0[i][j]+=(dp0[i-1][j]+dp0[i-1][j-1]*9)

    
  '''  
  if Nstr[i-1]!='0':
    for j in range(1,K+1):
      dp1[i][j]=dp1[i-1][j-1]
      dp0[i][j]+=(dp1[i-1][j-1]*(int(Nstr[i-1])-1)+dp1[i-1][j])
  else:
    for j in range(1,K+1):
      dp1[i][j]=dp1[i-1][j]
  for j in range(1,K+1):
    dp0[i][j]+=(dp0[i-1][j]+dp0[i-1][j-1]*9)
  '''
print(dp0[x][K]+dp1[x][K])

Buggy python submission (verdict: Runtime Error):
N=int(input())
K=int(input())
import math
x=math.floor(math.log10(N))+1
def combinations_count(n, r):
  return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
ans=0
if x<K:
  print(0)
  exit(0)
if K==1:
  ans=(x-1)*9
  ans+=(N//10**(x-1))
  print(ans)
elif K==2:
  for i in range(2,x):
    ans+=(9**2)*(i-1)
  f=(N//10**(x-1))
  n=str(N)
  for i in range(1,x):
    if n[i]!='0':
      s_n=x-i
      s=int(n[i])
      break
  ans+=(f-1)*9*(x-1)
  ans+=9*(s_n-1)
  ans+=s
  print(ans)
else:
  for i in range(3,x):
    ans+=(9**3)*combinations_count(i-1,2)
  f=(N//10**(x-1))
  n=str(N)
  s_n=0
  s=0
  t_n=0
  t=0
  for i in range(1,x):
    if n[i]!='0':
      s_n=x-i
      s=int(n[i])
      break
  for i in range(x-s_n+1,x):
    if n[i]!='0':
      t_n=x-i
      t=int(n[i])
      break
  if s_n<2:
    ans+=(f-1)*9**2*combinations_count(x-1,2)
    if s>0:
      ans+=(s-1)*9*(s_n-1)
    if t_n!=0:
      ans+=9*(t_n-1)
    ans+=t
  else:
    ans+=(f-1)*9**2*combinations_count(x-1,2)
    ans+=9**2*combinations_count(s_n-1,2)
    ans+=(s-1)*9*(s_n-1)
    if t_n!=0:
	    ans+=9*(t_n-1)
    ans+=t
  print(ans)

Fixed submission:
Nstr=input()
N=int(Nstr)
K=int(input())
x=len(Nstr)
dp0=[[0]*(K+1) for i in range(x+1)]
dp1=[[0]*(K+1) for i in range(x+1)]

dp1[0][0]=1

for i in range(1,x+1):
  dp0[i][0]=dp0[i-1][0]+dp1[i-1][0]
  for j in range(1,K+1):
    if Nstr[i-1]!='0':
      dp1[i][j]=dp1[i-1][j-1]
      dp0[i][j]+=(dp1[i-1][j-1]*(int(Nstr[i-1])-1)+dp1[i-1][j])
    else:
      dp1[i][j]=dp1[i-1][j]
    dp0[i][j]+=(dp0[i-1][j]+dp0[i-1][j-1]*9)

    
  '''  
  if Nstr[i-1]!='0':
    for j in range(1,K+1):
      dp1[i][j]=dp1[i-1][j-1]
      dp0[i][j]+=(dp1[i-1][j-1]*(int(Nstr[i-1])-1)+dp1[i-1][j])
  else:
    for j in range(1,K+1):
      dp1[i][j]=dp1[i-1][j]
  for j in range(1,K+1):
    dp0[i][j]+=(dp0[i-1][j]+dp0[i-1][j-1]*9)
  '''
print(dp0[x][K]+dp1[x][K])

Buggy python submission (verdict: Runtime Error):
N=int(input())
K=int(input())
import math
x=math.floor(math.log10(N))+1
def combinations_count(n, r):
  return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
ans=0
if x<K:
  print(0)
  exit(0)
if K==1:
  ans=(x-1)*9
  ans+=(N//10**(x-1))
  print(ans)
elif K==2:
  for i in range(2,x):
    ans+=(9**2)*(i-1)
  f=(N//10**(x-1))
  n=str(N)
  for i in range(1,x):
    if n[i]!='0':
      s_n=x-i
      s=int(n[i])
      break
  ans+=(f-1)*9*(x-1)
  ans+=9*(s_n-1)
  ans+=s
  print(ans)
else:
  for i in range(3,x):
    ans+=(9**3)*combinations_count(i-1,2)
  f=(N//10**(x-1))
  n=str(N)
  s_n=0
  t_n=0
  for i in range(1,x):
    if n[i]!='0':
      s_n=x-i
      s=int(n[i])
      break
  for i in range(x-s_n+1,x):
    if n[i]!='0':
      t_n=x-i
      t=int(n[i])
      break
  if s_n==2:
    ans+=(f-1)*9**2*combinations_count(x-1,2)
    ans+=(s-1)*9*(s_n-1)
    if t_n!=0:
      ans+=9*(t_n-1)
    ans+=t
  else:
    ans+=(f-1)*9**2*combinations_count(x-1,2)
    ans+=9**2*combinations_count(s_n-1,2)
    ans+=(s-1)*9*(s_n-1)
    if t_n!=0:
	    ans+=9*(t_n-1)
    ans+=t
  print(ans)

Fixed submission:
Nstr=input()
N=int(Nstr)
K=int(input())
x=len(Nstr)
dp0=[[0]*(K+1) for i in range(x+1)]
dp1=[[0]*(K+1) for i in range(x+1)]

dp1[0][0]=1

for i in range(1,x+1):
  dp0[i][0]=dp0[i-1][0]+dp1[i-1][0]
  for j in range(1,K+1):
    if Nstr[i-1]!='0':
      dp1[i][j]=dp1[i-1][j-1]
      dp0[i][j]+=(dp1[i-1][j-1]*(int(Nstr[i-1])-1)+dp1[i-1][j])
    else:
      dp1[i][j]=dp1[i-1][j]
    dp0[i][j]+=(dp0[i-1][j]+dp0[i-1][j-1]*9)

    
  '''  
  if Nstr[i-1]!='0':
    for j in range(1,K+1):
      dp1[i][j]=dp1[i-1][j-1]
      dp0[i][j]+=(dp1[i-1][j-1]*(int(Nstr[i-1])-1)+dp1[i-1][j])
  else:
    for j in range(1,K+1):
      dp1[i][j]=dp1[i-1][j]
  for j in range(1,K+1):
    dp0[i][j]+=(dp0[i-1][j]+dp0[i-1][j-1]*9)
  '''
print(dp0[x][K]+dp1[x][K])

Buggy python submission (verdict: Runtime Error):
N=int(input())
K=int(input())
import math
x=math.floor(math.log10(N))+1
def combinations_count(n, r):
  return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
ans=0
if x<K:
  print(0)
  exit(0)
if K==1:
  ans=(x-1)*9
  ans+=(N//10**(x-1))
  print(ans)
elif K==2:
  for i in range(2,x):
    ans+=(9**2)*(i-1)
  f=(N//10**(x-1))
  n=str(N)
  for i in range(1,x):
    if n[i]!='0':
      s_n=x-i
      s=int(n[i])
      break
  ans+=(f-1)*9*(x-1)
  ans+=9*(s_n-1)
  ans+=s
  print(ans)
else:
  for i in range(3,x):
    ans+=(9**3)*combinations_count(i-1,2)
  f=(N//10**(x-1))
  n=str(N)
  for i in range(1,x):
    if n[i]!='0':
      s_n=x-i
      s=int(n[i])
      break
  for i in range(x-s_n+1,x):
    if n[i]!='0':
      t_n=x-i
      t=int(n[i])
      break
  ans+=(f-1)*9**2*combinations_count(x-1,2)
  ans+=9**2*combinations_count(s_n-1,2)
  ans+=(s-1)*9*(s_n-1)
  ans+=9*(t_n-1)
  ans+=t
  print(ans)

Fixed submission:
Nstr=input()
N=int(Nstr)
K=int(input())
x=len(Nstr)
dp0=[[0]*(K+1) for i in range(x+1)]
dp1=[[0]*(K+1) for i in range(x+1)]

dp1[0][0]=1

for i in range(1,x+1):
  dp0[i][0]=dp0[i-1][0]+dp1[i-1][0]
  for j in range(1,K+1):
    if Nstr[i-1]!='0':
      dp1[i][j]=dp1[i-1][j-1]
      dp0[i][j]+=(dp1[i-1][j-1]*(int(Nstr[i-1])-1)+dp1[i-1][j])
    else:
      dp1[i][j]=dp1[i-1][j]
    dp0[i][j]+=(dp0[i-1][j]+dp0[i-1][j-1]*9)

    
  '''  
  if Nstr[i-1]!='0':
    for j in range(1,K+1):
      dp1[i][j]=dp1[i-1][j-1]
      dp0[i][j]+=(dp1[i-1][j-1]*(int(Nstr[i-1])-1)+dp1[i-1][j])
  else:
    for j in range(1,K+1):
      dp1[i][j]=dp1[i-1][j]
  for j in range(1,K+1):
    dp0[i][j]+=(dp0[i-1][j]+dp0[i-1][j-1]*9)
  '''
print(dp0[x][K]+dp1[x][K])

Buggy python submission (verdict: Runtime Error):
N=int(input())
K=int(input())
import math
x=math.floor(math.log10(N))+1
def combinations_count(n, r):
  return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
ans=0
if K==1:
  ans=(x-1)*9
  ans+=(N//10**(x-1))
  print(ans)
elif K==2:
  for i in range(2,x):
    ans+=(9**2)*(i-1)
  f=(N//10**(x-1))
  n=str(N)
  for i in range(1,x):
    if n[i]!='0':
      s_n=x-i
      s=int(n[i])
      break
  ans+=(f-1)*9*(x-1)
  ans+=9*(s_n-1)
  ans+=s
  print(ans)
else:
  for i in range(3,x):
    ans+=(9**3)*combinations_count(i-1,2)
  f=(N//10**(x-1))
  n=str(N)
  for i in range(1,x):
    if n[i]!='0':
      s_n=x-i
      s=int(n[i])
      break
  for i in range(x-s_n+1,x):
    if n[i]!='0':
      t_n=x-i
      t=int(n[i])
      break
  ans+=(f-1)*9**2*combinations_count(x-1,2)
  ans+=9**2*combinations_count(s_n-1,2)
  ans+=(s-1)*9*(s_n-1)
  ans+=9*(t_n-1)
  ans+=t
  print(ans)

Fixed submission:
Nstr=input()
N=int(Nstr)
K=int(input())
x=len(Nstr)
dp0=[[0]*(K+1) for i in range(x+1)]
dp1=[[0]*(K+1) for i in range(x+1)]

dp1[0][0]=1

for i in range(1,x+1):
  dp0[i][0]=dp0[i-1][0]+dp1[i-1][0]
  for j in range(1,K+1):
    if Nstr[i-1]!='0':
      dp1[i][j]=dp1[i-1][j-1]
      dp0[i][j]+=(dp1[i-1][j-1]*(int(Nstr[i-1])-1)+dp1[i-1][j])
    else:
      dp1[i][j]=dp1[i-1][j]
    dp0[i][j]+=(dp0[i-1][j]+dp0[i-1][j-1]*9)

    
  '''  
  if Nstr[i-1]!='0':
    for j in range(1,K+1):
      dp1[i][j]=dp1[i-1][j-1]
      dp0[i][j]+=(dp1[i-1][j-1]*(int(Nstr[i-1])-1)+dp1[i-1][j])
  else:
    for j in range(1,K+1):
      dp1[i][j]=dp1[i-1][j]
  for j in range(1,K+1):
    dp0[i][j]+=(dp0[i-1][j]+dp0[i-1][j-1]*9)
  '''
print(dp0[x][K]+dp1[x][K])