Buggy python submission (verdict: Time Limit Exceeded):
from itertools import product

MOD = 10**9 + 7
S = input()
N = len(S)
dp = [[0]*13 for _ in range(N+1)]
dp[0][0] = 1
for d in range(N):
    if S[d] == '?':
        for i, j in product(range(13), range(10)): # '?' = j
            rem = ((10 * i) % 13 + j) % 13
            dp[d + 1][rem] += dp[d][i]
            dp[d + 1][rem] %= MOD
    else:
        for i in range(13):
            rem = ((10 * i) % 13 + int(S[d])) % 13
            dp[d + 1][rem] += dp[d][i]
            dp[d + 1][rem] %= MOD
print(dp[N][5])

Fixed submission:
from itertools import product

MOD = 10**9 + 7
S = input()
N = len(S)
dp = [[0]*13 for _ in range(N+1)]
dp[0][0] = 1
for d in range(N):
    if S[d] == '?':
        for i, j in product(range(13), range(10)): # '?' = j
            rem = ((10 * i) % 13 + j) % 13
            dp[d + 1][rem] += dp[d][i]
            dp[d + 1][rem] %= MOD
    else:
        for i in range(13):
            rem = ((10 * i) % 13 + int(S[d])) % 13
            dp[d + 1][rem] += dp[d][i]
            dp[d + 1][rem] %= MOD
print(dp[N][5])

Buggy python submission (verdict: Time Limit Exceeded):
from itertools import product

MOD = 10**9 + 7
S = input()
N = len(S)
dp = [[0 for _ in range(13)] for _ in range(N+1)]
dp[0][0] = 1
for i in range(N):
    temp = 10**(N-i-1)
    if S[i] == '?':
        for j, k in product(range(13), range(10)):
            rem = (k * temp) % 13
            target = (j + rem) % 13
            dp[i+1][target] += dp[i][j]
            dp[i+1][target] %= MOD
    else:
        rem = (int(S[i]) * temp) % 13
        for j in range(13):
            target = (j + rem) % 13
            dp[i+1][target] += dp[i][j]
            dp[i+1][target] %= MOD
print(dp[N][5])

Fixed submission:
from itertools import product

MOD = 10**9 + 7
S = input()
N = len(S)
dp = [[0]*13 for _ in range(N+1)]
dp[0][0] = 1
for d in range(N):
    if S[d] == '?':
        for i, j in product(range(13), range(10)): # '?' = j
            rem = ((10 * i) % 13 + j) % 13
            dp[d + 1][rem] += dp[d][i]
            dp[d + 1][rem] %= MOD
    else:
        for i in range(13):
            rem = ((10 * i) % 13 + int(S[d])) % 13
            dp[d + 1][rem] += dp[d][i]
            dp[d + 1][rem] %= MOD
print(dp[N][5])

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

Fixed submission:
from itertools import product

MOD = 10**9 + 7
S = input()
N = len(S)
dp = [[0]*13 for _ in range(N+1)]
dp[0][0] = 1
for d in range(N):
    if S[d] == '?':
        for i, j in product(range(13), range(10)): # '?' = j
            rem = ((10 * i) % 13 + j) % 13
            dp[d + 1][rem] += dp[d][i]
            dp[d + 1][rem] %= MOD
    else:
        for i in range(13):
            rem = ((10 * i) % 13 + int(S[d])) % 13
            dp[d + 1][rem] += dp[d][i]
            dp[d + 1][rem] %= MOD
print(dp[N][5])

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

Fixed submission:
from itertools import product

MOD = 10**9 + 7
S = input()
N = len(S)
dp = [[0]*13 for _ in range(N+1)]
dp[0][0] = 1
for d in range(N):
    if S[d] == '?':
        for i, j in product(range(13), range(10)): # '?' = j
            rem = ((10 * i) % 13 + j) % 13
            dp[d + 1][rem] += dp[d][i]
            dp[d + 1][rem] %= MOD
    else:
        for i in range(13):
            rem = ((10 * i) % 13 + int(S[d])) % 13
            dp[d + 1][rem] += dp[d][i]
            dp[d + 1][rem] %= MOD
print(dp[N][5])