Buggy python submission (verdict: Time Limit Exceeded):
MOD1 = 13
MOD2 = 10 ** 9 + 7

S = input()
N = len(S)
dp = [[0 for _ in range(MOD1)] for _ in range(N)]

if S[0] == '?':
    for k in range(10):
        dp[0][k % MOD1] += 1
else:
    dp[0][int(S[0]) % MOD1] += 1

for i in range(N-1):
    if S[i+1] == '?':
        for j in range(MOD1):
            for k in range(10):
                tmp_j = (j * 10 + k) % MOD1
                dp[i+1][tmp_j] += dp[i][j]
    else:
        for j in range(MOD1):
            tmp_j = (j * 10 + int(S[i+1])) % MOD1
            dp[i+1][tmp_j] += dp[i][j]

print(dp[-1][5] % MOD2)


Fixed submission:
MOD1 = 13
MOD2 = 10 ** 9 + 7

S = input()
N = len(S)
dp = [[0 for _ in range(MOD1)] for _ in range(N)]

if S[0] == '?':
    for k in range(10):
        dp[0][k % MOD1] += 1
else:
    dp[0][int(S[0]) % MOD1] += 1

for i in range(N-1):
    if S[i+1] == '?':
        for j in range(MOD1):
            for k in range(10):
                tmp_j = (j * 10 + k) % MOD1
                dp[i+1][tmp_j] += dp[i][j]
                dp[i + 1][tmp_j] %= MOD2
    else:
        for j in range(MOD1):
            tmp_j = (j * 10 + int(S[i+1])) % MOD1
            dp[i+1][tmp_j] += dp[i][j]
            dp[i + 1][tmp_j] %= MOD2

print(dp[-1][5] % MOD2)

Buggy python submission (verdict: Time Limit Exceeded):
MOD1 = 13
MOD2 = 10 ** 9 + 7

S = input()
revS = S[::-1]
N = len(S)
dp = [[0 for _ in range(MOD1)] for _ in range(N)]

if revS[0] == '?':
    for k in range(10):
        dp[0][k % MOD1] += 1
else:
    dp[0][int(revS[0]) % MOD1] += 1

for i in range(1, N):
    if revS[i] == '?':
        for k in range(10):
            for j in range(MOD1):
                tmp_j = (k * 10 ** i % MOD1 + j) % MOD1
                dp[i][tmp_j] += dp[i - 1][j]
    else:
        for j in range(MOD1):
            tmp_j = (int(revS[i]) * 10 ** i % MOD1 + j) % MOD1
            dp[i][tmp_j] += dp[i - 1][j]

print(dp[-1][5] % MOD2)


Fixed submission:
MOD1 = 13
MOD2 = 10 ** 9 + 7

S = input()
N = len(S)
dp = [[0 for _ in range(MOD1)] for _ in range(N)]

if S[0] == '?':
    for k in range(10):
        dp[0][k % MOD1] += 1
else:
    dp[0][int(S[0]) % MOD1] += 1

for i in range(N-1):
    if S[i+1] == '?':
        for j in range(MOD1):
            for k in range(10):
                tmp_j = (j * 10 + k) % MOD1
                dp[i+1][tmp_j] += dp[i][j]
                dp[i + 1][tmp_j] %= MOD2
    else:
        for j in range(MOD1):
            tmp_j = (j * 10 + int(S[i+1])) % MOD1
            dp[i+1][tmp_j] += dp[i][j]
            dp[i + 1][tmp_j] %= MOD2

print(dp[-1][5] % MOD2)

Buggy python submission (verdict: Time Limit Exceeded):
MOD1 = 13
MOD2 = 10 ** 9 + 7

S = input()
revS = S[::-1]
N = len(S)
dp = [[0 for _ in range(MOD1)] for _ in range(N)]

if revS[0] == '?':
    for k in range(10):
        dp[0][k % MOD1] += 1
else:
    dp[0][int(revS[0]) % MOD1] += 1

for i in range(1, N):
    if revS[i] == '?':
        for k in range(10):
            for j in range(MOD1):
                tmp_j = (k * 10 ** i % MOD1 + j) % MOD1
                dp[i][tmp_j] += dp[i - 1][j]
                dp[i][tmp_j] %= MOD2
    else:
        for j in range(MOD1):
            tmp_j = (int(revS[i]) * 10 ** i % MOD1 + j) % MOD1
            dp[i][tmp_j] += dp[i - 1][j]
            dp[i][tmp_j] %= MOD2

print(dp[-1][5])


Fixed submission:
MOD1 = 13
MOD2 = 10 ** 9 + 7

S = input()
N = len(S)
dp = [[0 for _ in range(MOD1)] for _ in range(N)]

if S[0] == '?':
    for k in range(10):
        dp[0][k % MOD1] += 1
else:
    dp[0][int(S[0]) % MOD1] += 1

for i in range(N-1):
    if S[i+1] == '?':
        for j in range(MOD1):
            for k in range(10):
                tmp_j = (j * 10 + k) % MOD1
                dp[i+1][tmp_j] += dp[i][j]
                dp[i + 1][tmp_j] %= MOD2
    else:
        for j in range(MOD1):
            tmp_j = (j * 10 + int(S[i+1])) % MOD1
            dp[i+1][tmp_j] += dp[i][j]
            dp[i + 1][tmp_j] %= MOD2

print(dp[-1][5] % MOD2)

Buggy python submission (verdict: Time Limit Exceeded):
MOD1 = 13
MOD2 = 10 ** 9 + 7

S = input()
revS = S[::-1]
N = len(S)
dp = [[0 for _ in range(MOD1)] for _ in range(N)]

if revS[0] == '?':
    for k in range(10):
        dp[0][k % MOD1] += 1
else:
    dp[0][int(revS[0]) % MOD1] += 1

for i in range(1, N):
    if revS[i] == '?':
        for k in range(10):
            for j in range(MOD1):
                dp[i][(k * 10 ** i + j) % MOD1] += dp[i - 1][j]
                dp[i][(k * 10 ** i + j) % MOD1] %= MOD2

    else:
        for j in range(MOD1):
            dp[i][(int(revS[i]) * 10 ** i + j) % MOD1] += dp[i - 1][j]
            dp[i][(int(revS[i]) * 10 ** i + j) % MOD1] %= MOD2

print(dp[-1][5])


Fixed submission:
MOD1 = 13
MOD2 = 10 ** 9 + 7

S = input()
N = len(S)
dp = [[0 for _ in range(MOD1)] for _ in range(N)]

if S[0] == '?':
    for k in range(10):
        dp[0][k % MOD1] += 1
else:
    dp[0][int(S[0]) % MOD1] += 1

for i in range(N-1):
    if S[i+1] == '?':
        for j in range(MOD1):
            for k in range(10):
                tmp_j = (j * 10 + k) % MOD1
                dp[i+1][tmp_j] += dp[i][j]
                dp[i + 1][tmp_j] %= MOD2
    else:
        for j in range(MOD1):
            tmp_j = (j * 10 + int(S[i+1])) % MOD1
            dp[i+1][tmp_j] += dp[i][j]
            dp[i + 1][tmp_j] %= MOD2

print(dp[-1][5] % MOD2)

Buggy python submission (verdict: Time Limit Exceeded):
def is_match(str_num):
  for idx, num in nums.items():
    if str_num[idx] != num: return False
  return True

S = input()
lenS = len(S)
nums = {idx: s for idx, s in enumerate(S) if s != '?' }

MOD = 10**9 + 7
ans = 0

for i in range(int(S.replace('?', '9'))//13 + 1):
  num = i*13 + 5
  str_num = str(num).zfill(lenS)

  if is_match(str_num) is True:
    ans += 1
    ans = ans % MOD

print(ans%MOD)

Fixed submission:
MOD1 = 13
MOD2 = 10 ** 9 + 7

S = input()
N = len(S)
dp = [[0 for _ in range(MOD1)] for _ in range(N)]

if S[0] == '?':
    for k in range(10):
        dp[0][k % MOD1] += 1
else:
    dp[0][int(S[0]) % MOD1] += 1

for i in range(N-1):
    if S[i+1] == '?':
        for j in range(MOD1):
            for k in range(10):
                tmp_j = (j * 10 + k) % MOD1
                dp[i+1][tmp_j] += dp[i][j]
                dp[i + 1][tmp_j] %= MOD2
    else:
        for j in range(MOD1):
            tmp_j = (j * 10 + int(S[i+1])) % MOD1
            dp[i+1][tmp_j] += dp[i][j]
            dp[i + 1][tmp_j] %= MOD2

print(dp[-1][5] % MOD2)