Buggy python submission (verdict: Runtime Error):
import sys
input=lambda: sys.stdin.readline().rstrip()
mod=10**9+7
a,b,n=map(int,input().split())
def primes(x):
  is_prime=[True]*(x+1)
  is_prime[0]=False
  is_prime[1]=False
  for i in range(2,int(x**0.5)+1):
    if not is_prime[i]:
      continue
    for j in range(i*2,x+1,i):
      is_prime[j]=False
  return [i for i in range(x+1) if is_prime[i]]
P=primes(b)
ans=1
for p in P:
  ord=1
  ord_p=0
  while True:
    ct=b//(p**ord)-(a-1)//(p**ord)
    if ct:
      ord_p+=pow(ct,n,mod-1)
      ord+=1
    else:
      break
  ord_p%=mod-1
  ans=(ans*(pow(p,ord_p,mod)))%mod
print(ans)


Fixed submission:
mod=10**9+7
s=input()
n=len(s)
R=[[[0]*13 for _ in range(10)] for __ in range(13)]
for i in range(13):
  for j in range(10):
    for k in range(13):
      R[i][j][k]=(k-i*j)%13

P=[0]*(n+1)
P[0]=1
for i in range(n):
  P[i+1]=(P[i]*10)%13

DP=[[0]*13 for _ in range(n+1)]
DP[0][0]=1
for i in range(n):
  r=P[n-1-i]
  if s[i]=="?":
    for k in range(13):
      DP[i+1][k]=sum(DP[i][R[r][j][k]] for j in range(10))
      DP[i+1][k]%=mod
  else:
    for k in range(13):
      DP[i+1][k]=DP[i][R[r][int(s[i])][k]]
      DP[i+1][k]%=mod
print(DP[n][5]%mod)

Buggy python submission (verdict: Time Limit Exceeded):
mod=10**9+7
s=input()
n=len(s)
DP=[[0]*13 for _ in range(n+1)]
DP[0][0]=1
for i in range(n):
  r=pow(10,n-1-i,13)
  if s[i]=="?":
    for j in range(10):
      rr=(r*j)%13
      for k in range(13):
        if k>=rr:
          DP[i+1][k]+=DP[i][k-rr]
        else:
          DP[i+1][k]+=DP[i][k-rr+13]
        DP[i+1][k]%=mod
  else:
    rr=(r*int(s[i]))%13
    for k in range(13):
      if k>=rr:
        DP[i+1][k]+=DP[i][k-rr]
      else:
        DP[i+1][k]+=DP[i][k-rr+13]
      DP[i+1][k]%=mod
print(DP[n][5]%mod)


Fixed submission:
mod=10**9+7
s=input()
n=len(s)
R=[[[0]*13 for _ in range(10)] for __ in range(13)]
for i in range(13):
  for j in range(10):
    for k in range(13):
      R[i][j][k]=(k-i*j)%13

P=[0]*(n+1)
P[0]=1
for i in range(n):
  P[i+1]=(P[i]*10)%13

DP=[[0]*13 for _ in range(n+1)]
DP[0][0]=1
for i in range(n):
  r=P[n-1-i]
  if s[i]=="?":
    for k in range(13):
      DP[i+1][k]=sum(DP[i][R[r][j][k]] for j in range(10))
      DP[i+1][k]%=mod
  else:
    for k in range(13):
      DP[i+1][k]=DP[i][R[r][int(s[i])][k]]
      DP[i+1][k]%=mod
print(DP[n][5]%mod)

Buggy python submission (verdict: Time Limit Exceeded):
mod=10**9+7
s=input()
n=len(s)
DP=[[0]*13 for _ in range(n+1)]
DP[0][0]=1
for i in range(n):
  r=(10**(n-1-i))%13
  if s[i]=="?":
    for j in range(10):
      rr=(r*j)%13
      for k in range(13):
        if k>=rr:
          DP[i+1][k]+=DP[i][k-rr]
        else:
          DP[i+1][k]+=DP[i][k-rr+13]
        DP[i+1][k]%=mod
  else:
    rr=(r*int(s[i]))%13
    for k in range(13):
      if k>=rr:
        DP[i+1][k]+=DP[i][k-rr]
      else:
        DP[i+1][k]+=DP[i][k-rr+13]
      DP[i+1][k]%=mod
print(DP[n][5]%mod)


Fixed submission:
mod=10**9+7
s=input()
n=len(s)
R=[[[0]*13 for _ in range(10)] for __ in range(13)]
for i in range(13):
  for j in range(10):
    for k in range(13):
      R[i][j][k]=(k-i*j)%13

P=[0]*(n+1)
P[0]=1
for i in range(n):
  P[i+1]=(P[i]*10)%13

DP=[[0]*13 for _ in range(n+1)]
DP[0][0]=1
for i in range(n):
  r=P[n-1-i]
  if s[i]=="?":
    for k in range(13):
      DP[i+1][k]=sum(DP[i][R[r][j][k]] for j in range(10))
      DP[i+1][k]%=mod
  else:
    for k in range(13):
      DP[i+1][k]=DP[i][R[r][int(s[i])][k]]
      DP[i+1][k]%=mod
print(DP[n][5]%mod)

Buggy python submission (verdict: Time Limit Exceeded):
mod=10**9+7
s=input()
n=len(s)
DP=[[0]*13 for _ in range(n+1)]
DP[0][0]=1
for i in range(n):
  r=(10**(n-1-i))%13
  if s[i]=="?":
    for j in range(10):
      rr=(r*j)%13
      for k in range(13):
        if k>=rr:
          DP[i+1][k]+=DP[i][k-rr]
        else:
          DP[i+1][k]+=DP[i][k-rr+13]
        DP[i+1][k]%=mod
  else:
    rr=(r*int(s[i]))%13
    for k in range(13):
      if k>=rr:
        DP[i+1][k]+=DP[i][k-rr]
      else:
        DP[i+1][k]+=DP[i][k-rr+13]
      DP[i+1][k]%=mod
print(DP[n][5]%mod)


Fixed submission:
mod=10**9+7
s=input()
n=len(s)
R=[[[0]*13 for _ in range(10)] for __ in range(13)]
for i in range(13):
  for j in range(10):
    for k in range(13):
      R[i][j][k]=(k-i*j)%13

P=[0]*(n+1)
P[0]=1
for i in range(n):
  P[i+1]=(P[i]*10)%13

DP=[[0]*13 for _ in range(n+1)]
DP[0][0]=1
for i in range(n):
  r=P[n-1-i]
  if s[i]=="?":
    for k in range(13):
      DP[i+1][k]=sum(DP[i][R[r][j][k]] for j in range(10))
      DP[i+1][k]%=mod
  else:
    for k in range(13):
      DP[i+1][k]=DP[i][R[r][int(s[i])][k]]
      DP[i+1][k]%=mod
print(DP[n][5]%mod)

Buggy python submission (verdict: Time Limit Exceeded):
s=input()
n=len(s)
R=[[[0]*13 for _ in range(10)] for __ in range(13)]
for i in range(13):
  for j in range(10):
    for k in range(13):
      R[i][j][k]=(k-i*j)%13

P=[0]*(n+1)
P[0]=1
for i in range(n):
  P[i+1]=(P[i]*10)%13

DP=[[0]*13 for _ in range(n+1)]
DP[0][0]=1
for i in range(n):
  r=P[n-1-i]
  if s[i]=="?":
    for k in range(13):
      DP[i+1][k]=sum(DP[i][R[r][j][k]] for j in range(10))
  else:
    for k in range(13):
      DP[i+1][k]=DP[i][R[r][int(s[i])][k]]
print(DP[n][5]%(10**9+7))

Fixed submission:
mod=10**9+7
s=input()
n=len(s)
R=[[[0]*13 for _ in range(10)] for __ in range(13)]
for i in range(13):
  for j in range(10):
    for k in range(13):
      R[i][j][k]=(k-i*j)%13

P=[0]*(n+1)
P[0]=1
for i in range(n):
  P[i+1]=(P[i]*10)%13

DP=[[0]*13 for _ in range(n+1)]
DP[0][0]=1
for i in range(n):
  r=P[n-1-i]
  if s[i]=="?":
    for k in range(13):
      DP[i+1][k]=sum(DP[i][R[r][j][k]] for j in range(10))
      DP[i+1][k]%=mod
  else:
    for k in range(13):
      DP[i+1][k]=DP[i][R[r][int(s[i])][k]]
      DP[i+1][k]%=mod
print(DP[n][5]%mod)

Buggy python submission (verdict: Time Limit Exceeded):
s=input()
n=len(s)
R=[[[0]*13 for _ in range(10)] for __ in range(13)]
for i in range(13):
  for j in range(10):
    for k in range(13):
      R[i][j][k]=(k-i*j)%13

DP=[[0]*13 for _ in range(n+1)]
DP[0][0]=1
for i in range(n):
  r=pow(10,n-1-i,13)
  if s[i]=="?":
    for k in range(13):
      DP[i+1][k]=sum(DP[i][R[r][j][k]] for j in range(10))
  else:
    for k in range(13):
      DP[i+1][k]=DP[i][R[r][int(s[i])][k]]
print(DP[n][5]%(10**9+7))

Fixed submission:
mod=10**9+7
s=input()
n=len(s)
R=[[[0]*13 for _ in range(10)] for __ in range(13)]
for i in range(13):
  for j in range(10):
    for k in range(13):
      R[i][j][k]=(k-i*j)%13

P=[0]*(n+1)
P[0]=1
for i in range(n):
  P[i+1]=(P[i]*10)%13

DP=[[0]*13 for _ in range(n+1)]
DP[0][0]=1
for i in range(n):
  r=P[n-1-i]
  if s[i]=="?":
    for k in range(13):
      DP[i+1][k]=sum(DP[i][R[r][j][k]] for j in range(10))
      DP[i+1][k]%=mod
  else:
    for k in range(13):
      DP[i+1][k]=DP[i][R[r][int(s[i])][k]]
      DP[i+1][k]%=mod
print(DP[n][5]%mod)

Buggy python submission (verdict: Time Limit Exceeded):
s=input()
n=len(s)
R=[[[0]*13 for _ in range(10)] for __ in range(13)]
for i in range(13):
  for j in range(10):
    for k in range(13):
      R[i][j][k]=(k-i*j)%13

DP=[[0]*13 for _ in range(n+1)]
DP[0][0]=1
for i in range(n):
  r=pow(10,n-1-i,13)
  if s[i]=="?":
    for j in range(10):
      for k in range(13):
        DP[i+1][k]+=DP[i][R[r][j][k]]
  else:
    for k in range(13):
      DP[i+1][k]+=DP[i][R[r][int(s[i])][k]]
print(DP[n][5]%(10**9+7))

Fixed submission:
mod=10**9+7
s=input()
n=len(s)
R=[[[0]*13 for _ in range(10)] for __ in range(13)]
for i in range(13):
  for j in range(10):
    for k in range(13):
      R[i][j][k]=(k-i*j)%13

P=[0]*(n+1)
P[0]=1
for i in range(n):
  P[i+1]=(P[i]*10)%13

DP=[[0]*13 for _ in range(n+1)]
DP[0][0]=1
for i in range(n):
  r=P[n-1-i]
  if s[i]=="?":
    for k in range(13):
      DP[i+1][k]=sum(DP[i][R[r][j][k]] for j in range(10))
      DP[i+1][k]%=mod
  else:
    for k in range(13):
      DP[i+1][k]=DP[i][R[r][int(s[i])][k]]
      DP[i+1][k]%=mod
print(DP[n][5]%mod)

Buggy python submission (verdict: Time Limit Exceeded):
s=input()
n=len(s)
DP=[[0]*13 for _ in range(n+1)]
DP[0][0]=1
for i in range(n):
  r=pow(10,n-1-i,13)
  if s[i]=="?":
    for j in range(10):
      for k in range(13):
        DP[i+1][k]+=DP[i][(k-r*j)%13]
  else:
    for k in range(13):
      DP[i+1][k]+=DP[i][(k-r*int(s[i]))%13]
print(DP[n][5]%(10**9+7))

Fixed submission:
mod=10**9+7
s=input()
n=len(s)
R=[[[0]*13 for _ in range(10)] for __ in range(13)]
for i in range(13):
  for j in range(10):
    for k in range(13):
      R[i][j][k]=(k-i*j)%13

P=[0]*(n+1)
P[0]=1
for i in range(n):
  P[i+1]=(P[i]*10)%13

DP=[[0]*13 for _ in range(n+1)]
DP[0][0]=1
for i in range(n):
  r=P[n-1-i]
  if s[i]=="?":
    for k in range(13):
      DP[i+1][k]=sum(DP[i][R[r][j][k]] for j in range(10))
      DP[i+1][k]%=mod
  else:
    for k in range(13):
      DP[i+1][k]=DP[i][R[r][int(s[i])][k]]
      DP[i+1][k]%=mod
print(DP[n][5]%mod)

Buggy python submission (verdict: Time Limit Exceeded):
s=input()
n=len(s)
DP=[[0]*13 for _ in range(n+1)]
DP[0][0]=1
for i in range(n):
  r=pow(10,n-1-i,13)
  if s[i]=="?":
    for j in range(10):
      rr=(r*j)%13
      for k in range(13):
        if k>=rr:
          DP[i+1][k]+=DP[i][k-rr]
        else:
          DP[i+1][k]+=DP[i][k-rr+13]
  else:
    rr=(r*int(s[i]))%13
    for k in range(13):
      if k>=rr:
        DP[i+1][k]+=DP[i][k-rr]
      else:
        DP[i+1][k]+=DP[i][k-rr+13]
print(DP[n][5]%(10**9+7))

Fixed submission:
mod=10**9+7
s=input()
n=len(s)
R=[[[0]*13 for _ in range(10)] for __ in range(13)]
for i in range(13):
  for j in range(10):
    for k in range(13):
      R[i][j][k]=(k-i*j)%13

P=[0]*(n+1)
P[0]=1
for i in range(n):
  P[i+1]=(P[i]*10)%13

DP=[[0]*13 for _ in range(n+1)]
DP[0][0]=1
for i in range(n):
  r=P[n-1-i]
  if s[i]=="?":
    for k in range(13):
      DP[i+1][k]=sum(DP[i][R[r][j][k]] for j in range(10))
      DP[i+1][k]%=mod
  else:
    for k in range(13):
      DP[i+1][k]=DP[i][R[r][int(s[i])][k]]
      DP[i+1][k]%=mod
print(DP[n][5]%mod)

Buggy python submission (verdict: Time Limit Exceeded):
s=input()
n=len(s)
DP=[[0]*13 for _ in range(n+1)]
DP[0][0]=1
for i in range(n):
  r=(10**(n-1-i))%13
  if s[i]=="?":
    for j in range(10):
      rr=(r*j)%13
      for k in range(13):
        if k>=rr:
          DP[i+1][k]+=DP[i][k-rr]
        else:
          DP[i+1][k]+=DP[i][k-rr+13]
  else:
    rr=(r*int(s[i]))%13
    for k in range(13):
      if k>=rr:
        DP[i+1][k]+=DP[i][k-rr]
      else:
        DP[i+1][k]+=DP[i][k-rr+13]
print(DP[n][5]%(10**9+7))

Fixed submission:
mod=10**9+7
s=input()
n=len(s)
R=[[[0]*13 for _ in range(10)] for __ in range(13)]
for i in range(13):
  for j in range(10):
    for k in range(13):
      R[i][j][k]=(k-i*j)%13

P=[0]*(n+1)
P[0]=1
for i in range(n):
  P[i+1]=(P[i]*10)%13

DP=[[0]*13 for _ in range(n+1)]
DP[0][0]=1
for i in range(n):
  r=P[n-1-i]
  if s[i]=="?":
    for k in range(13):
      DP[i+1][k]=sum(DP[i][R[r][j][k]] for j in range(10))
      DP[i+1][k]%=mod
  else:
    for k in range(13):
      DP[i+1][k]=DP[i][R[r][int(s[i])][k]]
      DP[i+1][k]%=mod
print(DP[n][5]%mod)

Buggy python submission (verdict: Time Limit Exceeded):
s=input()
n=len(s)
DP=[[0]*13 for _ in range(n+1)]
DP[0][0]=1
for i in range(n):
  r=(10**(n-1-i))%13
  if s[i]=="?":
    for j in range(10):
      rr=(r*j)%13
      for k in range(13):
        if k>=rr:
          DP[i+1][k]+=DP[i][k-rr]
        else:
          DP[i+1][k]+=DP[i][k-rr+13]
  else:
    rr=(r*int(s[i]))%13
    for k in range(13):
      if k>=rr:
        DP[i+1][k]+=DP[i][k-rr]
      else:
        DP[i+1][k]+=DP[i][k-rr+13]
print(DP[n][5]%(10**9+7))

Fixed submission:
mod=10**9+7
s=input()
n=len(s)
R=[[[0]*13 for _ in range(10)] for __ in range(13)]
for i in range(13):
  for j in range(10):
    for k in range(13):
      R[i][j][k]=(k-i*j)%13

P=[0]*(n+1)
P[0]=1
for i in range(n):
  P[i+1]=(P[i]*10)%13

DP=[[0]*13 for _ in range(n+1)]
DP[0][0]=1
for i in range(n):
  r=P[n-1-i]
  if s[i]=="?":
    for k in range(13):
      DP[i+1][k]=sum(DP[i][R[r][j][k]] for j in range(10))
      DP[i+1][k]%=mod
  else:
    for k in range(13):
      DP[i+1][k]=DP[i][R[r][int(s[i])][k]]
      DP[i+1][k]%=mod
print(DP[n][5]%mod)