Buggy python submission (verdict: Time Limit Exceeded):
S = input()
dp0 = [0]*13
dp0[0] = 1
dp = [dp0]
#print(dp[0])
for i in range(len(S)):
  dpi = dp[i]
  dpn = [0]*13
  c = S[i]
  e = (10**((len(S)-i-1)%12))%13
  if c == "?":
    for j in range(13):
      r = 0
      for d in range(10):
        r += dpi[(j+13-d*e)%13]
      dpn[j] = r%1000000007
  else:
    d = int(c)
    for j in range(13):
      dpn[j] = dpi[(j+13-d*e)%13]
  #print(dp[i+1])
  dp.append(dpn)
print(dp[len(S)][5])


Fixed submission:
S = input()
dp0 = [0]*13
dp0[0] = 1
dp = [dp0]
#print(dp[0])
for i in range(len(S)):
  dpi = dp[i]
  dpn = [0]*13
  c = S[i]
  e = (10**((len(S)-i-1)%12))%13
  if c == "?":
    for j in range(13):
      r = 0
      for d in range(10):
        r += dpi[(j+13-d*e)%13]
      dpn[j] = r%1000000007
  else:
    d = int(c)
    for j in range(13):
      dpn[j] = dpi[(j+13-d*e)%13]
  #print(dp[i+1])
  dp.append(dpn)
print(dp[len(S)][5])

Buggy python submission (verdict: Time Limit Exceeded):
S = input()
dp = [[0]*13 for i in range(len(S)+1)]
dp[0][0] = 1
#print(dp[0])
for i in range(len(S)):
  c = S[i]
  e = (10**((len(S)-i-1)%12))%13
  if c == "?":
    for j in range(13):
      r = 0
      for d in range(10):
        n = (d*e)%13
        r += dp[i][(j+13-n)%13]
      dp[i+1][j] = r%1000000007
  else:
    d = int(c)
    n = (d*e)%13
    for j in range(13):
      dp[i+1][j] = dp[i][(j+13-n)%13]
  #print(dp[i+1])
print(dp[len(S)][5])


Fixed submission:
S = input()
dp0 = [0]*13
dp0[0] = 1
dp = [dp0]
#print(dp[0])
for i in range(len(S)):
  dpi = dp[i]
  dpn = [0]*13
  c = S[i]
  e = (10**((len(S)-i-1)%12))%13
  if c == "?":
    for j in range(13):
      r = 0
      for d in range(10):
        r += dpi[(j+13-d*e)%13]
      dpn[j] = r%1000000007
  else:
    d = int(c)
    for j in range(13):
      dpn[j] = dpi[(j+13-d*e)%13]
  #print(dp[i+1])
  dp.append(dpn)
print(dp[len(S)][5])

Buggy python submission (verdict: Time Limit Exceeded):
S = input()
dp = [[0]*13 for i in range(len(S)+1)]
dp[0][0] = 1
#print(dp[0])
for i in range(len(S)):
  c = S[i]
  e = (10**((len(S)-i-1)%12))%13
  if c == "?":
    for d in range(10):
      n = (d*e)%13
      for j in range(13):
        dp[i+1][j] = (dp[i+1][j]+dp[i][(j+13-n)%13])%1000000007
  else:
    d = int(c)
    n = (d*e)%13
    for j in range(13):
      dp[i+1][j] = dp[i][(j+13-n)%13]
  #print(dp[i+1])
print(dp[len(S)][5])


Fixed submission:
S = input()
dp0 = [0]*13
dp0[0] = 1
dp = [dp0]
#print(dp[0])
for i in range(len(S)):
  dpi = dp[i]
  dpn = [0]*13
  c = S[i]
  e = (10**((len(S)-i-1)%12))%13
  if c == "?":
    for j in range(13):
      r = 0
      for d in range(10):
        r += dpi[(j+13-d*e)%13]
      dpn[j] = r%1000000007
  else:
    d = int(c)
    for j in range(13):
      dpn[j] = dpi[(j+13-d*e)%13]
  #print(dp[i+1])
  dp.append(dpn)
print(dp[len(S)][5])

Buggy python submission (verdict: Time Limit Exceeded):
S = input()
dp = [[0]*13 for i in range(len(S)+1)]
dp[0][0] = 1
#print(dp[0])
for i in range(len(S)):
  c = S[i]
  if c == "?":
    for d in range(10):
      n = (d*(10**((len(S)-i-1)%12)))%13
      for j in range(13):
        dp[i+1][j] = (dp[i+1][j]+dp[i][(j+13-n)%13])%1000000007
  else:
    d = int(c)
    n = (d*(10**((len(S)-i-1)%12)))%13
    for j in range(13):
      dp[i+1][j] = dp[i][(j+13-n)%13]
  #print(dp[i+1])
print(dp[len(S)][5])


Fixed submission:
S = input()
dp0 = [0]*13
dp0[0] = 1
dp = [dp0]
#print(dp[0])
for i in range(len(S)):
  dpi = dp[i]
  dpn = [0]*13
  c = S[i]
  e = (10**((len(S)-i-1)%12))%13
  if c == "?":
    for j in range(13):
      r = 0
      for d in range(10):
        r += dpi[(j+13-d*e)%13]
      dpn[j] = r%1000000007
  else:
    d = int(c)
    for j in range(13):
      dpn[j] = dpi[(j+13-d*e)%13]
  #print(dp[i+1])
  dp.append(dpn)
print(dp[len(S)][5])

Buggy python submission (verdict: Time Limit Exceeded):
S = input()
dp = [[0]*13 for i in range(len(S)+1)]
dp[0][0] = 1
#print(dp[0])
for i in range(len(S)):
  c = S[i]
  if c == "?":
    for d in range(10):
      n = (d*(10**(len(S)-i-1)))%13
      for j in range(13):
        dp[i+1][j] += dp[i][(j+13-n)%13]
  else:
    n = (int(c)*(10**(len(S)-i-1)))%13
    for j in range(13):
      dp[i+1][j] = dp[i][(j+13-n)%13]
  for j in range(13):
    dp[i+1][j] = dp[i+1][j]%1000000007
  #print(dp[i+1])
print(dp[len(S)][5])


Fixed submission:
S = input()
dp0 = [0]*13
dp0[0] = 1
dp = [dp0]
#print(dp[0])
for i in range(len(S)):
  dpi = dp[i]
  dpn = [0]*13
  c = S[i]
  e = (10**((len(S)-i-1)%12))%13
  if c == "?":
    for j in range(13):
      r = 0
      for d in range(10):
        r += dpi[(j+13-d*e)%13]
      dpn[j] = r%1000000007
  else:
    d = int(c)
    for j in range(13):
      dpn[j] = dpi[(j+13-d*e)%13]
  #print(dp[i+1])
  dp.append(dpn)
print(dp[len(S)][5])