Buggy python submission (verdict: Time Limit Exceeded):
import sys
s= sys.stdin.readline().strip()
mod=10**9+7
n=13
dp=[0]*n
mul=1
dp[0]=1
for c in reversed(s):
  ndp=[0]*n
  if c=='?':
    for k in range(10):
      k*=mul
      for j in range(n):
        t=(k+j)%n
        ndp[t]+=dp[j]
        ndp[t]%=mod
  else:
    k=int(c)*mul
    for j in range(n):
      t=(k+j)%n
      ndp[t]+=dp[j]
      ndp[t]%=mod
  mul*=10
  mul%=n
  dp=ndp
print(dp[5])


Fixed submission:
M=10**9+7
r=[[(j-k)*9%13for j in range(10)]for k in range(13)]
d=[1]+[0]*12
for c in input():
  d = [sum(d[j]for j in k)%M for k in r] if c>'9' else [d[(int(c)-k)*9%13]for k in range(13)]
print(d[5])

Buggy python submission (verdict: Time Limit Exceeded):
import sys
s= sys.stdin.readline().strip()
mod=10**9+7
n=13
dp=[0]*n
mul=1
dp[0]=1
for c in reversed(s):
  ndp=[0]*n
  if c=='?':
    for k in range(10):
      for j in range(n):
        ndp[(k*mul+j)%n]+=dp[j]
        ndp[(k*mul+j)%n]%=mod
  else:
    k=int(c)
    for j in range(n):
      ndp[(k*mul+j)%n]+=dp[j]
      ndp[(k*mul+j)%n]%=mod
  mul*=10
  mul%=n
  dp=ndp
print(dp[5])


Fixed submission:
M=10**9+7
r=[[(j-k)*9%13for j in range(10)]for k in range(13)]
d=[1]+[0]*12
for c in input():
  d = [sum(d[j]for j in k)%M for k in r] if c>'9' else [d[(int(c)-k)*9%13]for k in range(13)]
print(d[5])

Buggy python submission (verdict: Time Limit Exceeded):
s=input()[::-1]
mod=10**9+7
n=13
dp=[0]*n
mul=1
dp[0]=1
for c in s:
  ndp=[0]*n
  if c=='?':
    for k in range(10):
      for j in range(n):
        ndp[(k*mul+j)%n]=(ndp[(k*mul+j)%n]+dp[j])%mod
        #ndp[(k*mul+j)%n]%=mod
  else:
    k=int(c)
    for j in range(n):
      ndp[(k*mul+j)%n]=(ndp[(k*mul+j)%n]+dp[j])%mod
      #ndp[(k*mul+j)%n]%=mod
  mul*=10
  mul%=n
  dp=ndp
print(dp[5])


Fixed submission:
M=10**9+7
r=[[(j-k)*9%13for j in range(10)]for k in range(13)]
d=[1]+[0]*12
for c in input():
  d = [sum(d[j]for j in k)%M for k in r] if c>'9' else [d[(int(c)-k)*9%13]for k in range(13)]
print(d[5])

Buggy python submission (verdict: Time Limit Exceeded):
s=input()[::-1]
mod=10**9+7
n=13
dp=[0]*n
mul=1
dp[0]=1
for c in s:
  ndp=[0]*n
  if c=='?':
    for k in range(10):
      for j in range(n):
        ndp[(k*mul+j)%n]+=dp[j]
        ndp[(k*mul+j)%n]%=mod
  else:
    k=int(c)
    for j in range(n):
      ndp[(k*mul+j)%n]+=dp[j]
      ndp[(k*mul+j)%n]%=mod
  mul*=10
  mul%=n
  dp=ndp
print(dp[5])


Fixed submission:
M=10**9+7
r=[[(j-k)*9%13for j in range(10)]for k in range(13)]
d=[1]+[0]*12
for c in input():
  d = [sum(d[j]for j in k)%M for k in r] if c>'9' else [d[(int(c)-k)*9%13]for k in range(13)]
print(d[5])

Buggy python submission (verdict: Time Limit Exceeded):
s=input()[::-1]
mod=10**9+7
n=13
dp=[0]*n
mul=1
dp[0]=1
for c in s:
  ndp=[0]*n
  if c=='?':
    for k in range(10):
      for j in range(n):
        ndp[(k*mul+j)%n]+=dp[j]
        ndp[(k*mul+j)%n]%=mod
  else:
    k=int(c)
    for j in range(n):
      ndp[(k*mul+j)%n]+=dp[j]
      ndp[(k*mul+j)%n]%=mod
  mul*=10
  mul%=n
  dp=ndp
print(dp[5])


Fixed submission:
M=10**9+7
r=[[(j-k)*9%13for j in range(10)]for k in range(13)]
d=[1]+[0]*12
for c in input():
  d = [sum(d[j]for j in k)%M for k in r] if c>'9' else [d[(int(c)-k)*9%13]for k in range(13)]
print(d[5])