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

Fixed submission:
S = input()
#S = "19?04??????451??" * (10 ** 5 // 5)
mod = 10 ** 9 + 7
dp = [[0 for _ in range(13)] for _ in range(len(S))]
if S[0] == "?":
  for i in range(10):
    dp[0][i] = 1
else:
  dp[0][int(S[0])] = 1
#print(dp)
for i in range(len(S) - 1):
  if S[i + 1] == "?":
    for j in range(13):
      for k in range(10):
        dp[i + 1][(j * 10 + k) % 13] += dp[i][j] % mod
  else:
    for j in range(13):
      dp[i + 1][(j * 10 + int(S[i + 1])) % 13] += dp[i][j] % mod
#print(dp)
print(dp[len(S) - 1][5] % (10 ** 9 + 7))

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

Fixed submission:
S = input()
#S = "19?04??????451??" * (10 ** 5 // 5)
mod = 10 ** 9 + 7
dp = [[0 for _ in range(13)] for _ in range(len(S))]
if S[0] == "?":
  for i in range(10):
    dp[0][i] = 1
else:
  dp[0][int(S[0])] = 1
#print(dp)
for i in range(len(S) - 1):
  if S[i + 1] == "?":
    for j in range(13):
      for k in range(10):
        dp[i + 1][(j * 10 + k) % 13] += dp[i][j] % mod
  else:
    for j in range(13):
      dp[i + 1][(j * 10 + int(S[i + 1])) % 13] += dp[i][j] % mod
#print(dp)
print(dp[len(S) - 1][5] % (10 ** 9 + 7))

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

Fixed submission:
S = input()
#S = "19?04??????451??" * (10 ** 5 // 5)
mod = 10 ** 9 + 7
dp = [[0 for _ in range(13)] for _ in range(len(S))]
if S[0] == "?":
  for i in range(10):
    dp[0][i] = 1
else:
  dp[0][int(S[0])] = 1
#print(dp)
for i in range(len(S) - 1):
  if S[i + 1] == "?":
    for j in range(13):
      for k in range(10):
        dp[i + 1][(j * 10 + k) % 13] += dp[i][j] % mod
  else:
    for j in range(13):
      dp[i + 1][(j * 10 + int(S[i + 1])) % 13] += dp[i][j] % mod
#print(dp)
print(dp[len(S) - 1][5] % (10 ** 9 + 7))

Buggy python submission (verdict: Time Limit Exceeded):
S = input()
#print(S)
dp = [[0 for _ in range(13)] for _ in range(len(S))]
temp = 0

while dp[len(S) - 1][5] == 0:
  #print(dp)
  if temp == len(S):
    break
  for i in range(13):
    if temp == 0:
      #print(temp, i, S[temp])
      if S[temp] == "?":
        if i <= 9:
          dp[temp][i] = 1
      elif int(S[temp]) == i:
        dp[temp][i] = 1
      continue
    if S[temp] == "?":
      for j in range(13):
        if not i in {(j * 10 + k) % 13 for k in range(10)}:
          continue
        #print(temp, i, j, S[temp])
        dp[temp][i] += dp[temp - 1][j]
    else:
      j = 0
      for k in range(13):
        if (k * 10 + int(S[temp])) % 13 == i:
          j = k
          break
      dp[temp][i] += dp[temp - 1][j]
    dp[temp][i] %= 10 ** 9 + 7
  temp += 1
#print(dp)
print(dp[len(S) - 1][5])

Fixed submission:
S = input()
#S = "19?04??????451??" * (10 ** 5 // 5)
mod = 10 ** 9 + 7
dp = [[0 for _ in range(13)] for _ in range(len(S))]
if S[0] == "?":
  for i in range(10):
    dp[0][i] = 1
else:
  dp[0][int(S[0])] = 1
#print(dp)
for i in range(len(S) - 1):
  if S[i + 1] == "?":
    for j in range(13):
      for k in range(10):
        dp[i + 1][(j * 10 + k) % 13] += dp[i][j] % mod
  else:
    for j in range(13):
      dp[i + 1][(j * 10 + int(S[i + 1])) % 13] += dp[i][j] % mod
#print(dp)
print(dp[len(S) - 1][5] % (10 ** 9 + 7))

Buggy python submission (verdict: Time Limit Exceeded):
S = input()
#print(S)
dp = [[0 for _ in range(13)] for _ in range(len(S))]
temp = 0

while dp[len(S) - 1][5] == 0:
  #print(dp)
  if temp == len(S):
    break
  for i in range(13):
    if temp == 0:
      #print(temp, i, S[temp])
      if S[temp] == "?":
        if i <= 9:
          dp[temp][i] = 1
      elif int(S[temp]) == i:
        dp[temp][i] = 1
      continue
    if S[temp] == "?":
      for j in range(13):
        if not i in {(j * 10 + k) % 13 for k in range(10)}:
          continue
        #print(temp, i, j, S[temp])
        dp[temp][i] += dp[temp - 1][j]
    else:
      j = 0
      for k in range(13):
        if (k * 10 + int(S[temp])) % 13 == i:
          j = k
          break
      dp[temp][i] += dp[temp - 1][j]
    dp[temp][i] %= 10 ** 9 + 7
  temp += 1
#print(dp)
print(dp[len(S) - 1][5])

Fixed submission:
S = input()
#S = "19?04??????451??" * (10 ** 5 // 5)
mod = 10 ** 9 + 7
dp = [[0 for _ in range(13)] for _ in range(len(S))]
if S[0] == "?":
  for i in range(10):
    dp[0][i] = 1
else:
  dp[0][int(S[0])] = 1
#print(dp)
for i in range(len(S) - 1):
  if S[i + 1] == "?":
    for j in range(13):
      for k in range(10):
        dp[i + 1][(j * 10 + k) % 13] += dp[i][j] % mod
  else:
    for j in range(13):
      dp[i + 1][(j * 10 + int(S[i + 1])) % 13] += dp[i][j] % mod
#print(dp)
print(dp[len(S) - 1][5] % (10 ** 9 + 7))