Buggy python submission (verdict: Time Limit Exceeded):
MOD = 1000000007

s = [-1 if x == '?' else int(x) for x in input()]
n = len(s) + 1

dp = [0] * 13
dp[0] = 1

for i, x in enumerate(s):
    next_dp = [0] * 13
    if x == -1:
        for j in range(10):
            for ki in range(13):
                next_dp[(ki * 10 + j) % 13] += dp[ki]
    else:
        for ki in range(13):
                next_dp[(ki * 10 + x) % 13] += dp[ki]
    dp = [k % MOD for k in next_dp]

print(dp[5])

Fixed submission:
MOD = 1000000007

s = [-1 if x == '?' else int(x) for x in input()]
n = len(s) + 1

dp = [0] * 13
dp[0] = 1

r = [[(j-i)*4%13 for i in range(10)]for j in range(13)]

for i, x in enumerate(s):
    next_dp = [0] * 13
    if x == -1:
        next_dp = [sum(dp[i] for i in j) for j in r]
    else:
        next_dp = [dp[j[x]] for j in r]
    dp = [k % MOD for k in next_dp]

print(dp[5])

Buggy python submission (verdict: Time Limit Exceeded):
MOD = 1000000007

s = [-1 if x == '?' else int(x) for x in input()]
n = len(s) + 1

dp = [0] * 13
dp[0] = 1

for i, x in enumerate(s):
    next_dp = [0] * 13
    for j in range(10):
        if (x == -1) or (x == j):
            for ki in range(13):
                next_dp[(ki * 10 + j) % 13] += dp[ki]
    dp = [k % MOD for k in next_dp]

print(dp[5])

Fixed submission:
MOD = 1000000007

s = [-1 if x == '?' else int(x) for x in input()]
n = len(s) + 1

dp = [0] * 13
dp[0] = 1

r = [[(j-i)*4%13 for i in range(10)]for j in range(13)]

for i, x in enumerate(s):
    next_dp = [0] * 13
    if x == -1:
        next_dp = [sum(dp[i] for i in j) for j in r]
    else:
        next_dp = [dp[j[x]] for j in r]
    dp = [k % MOD for k in next_dp]

print(dp[5])

Buggy python submission (verdict: Time Limit Exceeded):
MOD = 1000000007

s = [-1 if x == '?' else int(x) for x in input()]
n = len(s) + 1

dp = [[0 for x in range(13)] for c in range(n)]
dp[0][0] = 1

for i, x in enumerate(s):
    for j in range(10):
        if (x == -1) or (x == j):
            for ki in range(13):
                dp[i+1][(ki * 10 + j) % 13] += dp[i][ki]
    dp[i+1] = [k % MOD for k in dp[i+1]]

print(dp[len(s)][5])

Fixed submission:
MOD = 1000000007

s = [-1 if x == '?' else int(x) for x in input()]
n = len(s) + 1

dp = [0] * 13
dp[0] = 1

r = [[(j-i)*4%13 for i in range(10)]for j in range(13)]

for i, x in enumerate(s):
    next_dp = [0] * 13
    if x == -1:
        next_dp = [sum(dp[i] for i in j) for j in r]
    else:
        next_dp = [dp[j[x]] for j in r]
    dp = [k % MOD for k in next_dp]

print(dp[5])

Buggy python submission (verdict: Time Limit Exceeded):
MOD = 1000000007

s = input()
n = len(s) + 1

dp = [[0 for x in range(13)] for c in range(n)]
dp[0][0] = 1

for i, x in enumerate(s):
    if x == '?':
        x = -1
    else:
        x = int(x)

    for j in range(10):
        if (x == -1) or (x == j):
            for ki in range(13):
                dp[i+1][(ki * 10 + j) % 13] += dp[i][ki]
    dp[i+1] = [k % MOD for k in dp[i+1]]

print(dp[len(s)][5])

Fixed submission:
MOD = 1000000007

s = [-1 if x == '?' else int(x) for x in input()]
n = len(s) + 1

dp = [0] * 13
dp[0] = 1

r = [[(j-i)*4%13 for i in range(10)]for j in range(13)]

for i, x in enumerate(s):
    next_dp = [0] * 13
    if x == -1:
        next_dp = [sum(dp[i] for i in j) for j in r]
    else:
        next_dp = [dp[j[x]] for j in r]
    dp = [k % MOD for k in next_dp]

print(dp[5])

Buggy python submission (verdict: Time Limit Exceeded):
s = [x for x in input()]

q_pos = [i if x == '?' else None for i, x in enumerate(s)]
q_pos = [x for x in q_pos if x is not None]

q_size = len(q_pos)
ans = 0
for i in range(10 ** q_size):
    r = [x for x in str(i).zfill(q_size)]
    for i_q, r_q in zip(q_pos, r):
        s[i_q] = r_q
    if (int(''.join(s)) - 5) % 13 == 0:
        ans += 1

print(ans % (10**9 + 7))

Fixed submission:
MOD = 1000000007

s = [-1 if x == '?' else int(x) for x in input()]
n = len(s) + 1

dp = [0] * 13
dp[0] = 1

r = [[(j-i)*4%13 for i in range(10)]for j in range(13)]

for i, x in enumerate(s):
    next_dp = [0] * 13
    if x == -1:
        next_dp = [sum(dp[i] for i in j) for j in r]
    else:
        next_dp = [dp[j[x]] for j in r]
    dp = [k % MOD for k in next_dp]

print(dp[5])