Buggy python submission (verdict: Time Limit Exceeded):
S = input()
dp = [[0]*13 for i in range(len(S)+1)]
MOD = 10**9+7

dp[0][0] = 1

for i, c in enumerate(S[::-1], 1):
    t = (10 ** (i-1)) % 13
    for j in range(13):
        if c == "?":
            for k in range(10):
                nj = (k*t+j) % 13
                dp[i][nj] += dp[i-1][j]
                dp[i][nj] %= MOD
        else:
            nj = (int(c)*t+j) % 13
            dp[i][nj] += dp[i-1][j]
            dp[i][nj] %= MOD
print(dp[-1][5])

Fixed submission:
from sys import stdin
S = (stdin.readline().rstrip())
dp = [[0]*13 for i in range(len(S)+1)]
MOD = 10**9+7
 
S = list(reversed(S))
dp[0][0] = 1
 
t = 1
for i, c in enumerate(S, 1):
    for j in range(13):
        if c == "?":
            for k in range(10):
                nj = (k*t+j) % 13
                dp[i][nj] = dp[i][nj] + dp[i-1][j]
                dp[i][nj] %= MOD
        else:
            nj = (int(c)*t+j) % 13
            dp[i][nj] = dp[i][nj] + dp[i-1][j]
            dp[i][nj] %= MOD
    t = (t*10)%13
print(dp[-1][5])

Buggy python submission (verdict: Time Limit Exceeded):
S = input()
dp = [[0]*13 for i in range(len(S)+1)]
MOD = 10**9+7

a = [0] + [(10**i) % 13 for i in range(len(S))]
dp[0][0] = 1

cnt = 1
for i, c in enumerate(S[::-1], 1):
    t = a[i]
    for j in range(13):
        if c == "?":
            for k in range(10):
                nj = (k*t+j) % 13
                dp[i][nj] = dp[i][nj] + dp[i-1][j]
                dp[i][nj] %= MOD
        else:
            nj = (int(c)*t+j) % 13
            dp[i][nj] = dp[i][nj] + dp[i-1][j]
            dp[i][nj] %= MOD
print(dp[-1][5])

Fixed submission:
from sys import stdin
S = (stdin.readline().rstrip())
dp = [[0]*13 for i in range(len(S)+1)]
MOD = 10**9+7
 
S = list(reversed(S))
dp[0][0] = 1
 
t = 1
for i, c in enumerate(S, 1):
    for j in range(13):
        if c == "?":
            for k in range(10):
                nj = (k*t+j) % 13
                dp[i][nj] = dp[i][nj] + dp[i-1][j]
                dp[i][nj] %= MOD
        else:
            nj = (int(c)*t+j) % 13
            dp[i][nj] = dp[i][nj] + dp[i-1][j]
            dp[i][nj] %= MOD
    t = (t*10)%13
print(dp[-1][5])

Buggy python submission (verdict: Time Limit Exceeded):
from sys import stdin
S = (stdin.readline().rstrip())
dp = [[0]*13 for i in range(len(S)+1)]
MOD = 10**9+7

a = [0] + [(10**i) % 13 for i in range(len(S))]
dp[0][0] = 1

cnt = 1
for i, c in enumerate(S[::-1], 1):
    for j in range(13):
        if c == "?":
            for k in range(10):
                nj = (k*a[i]+j) % 13
                dp[i][nj] = dp[i][nj] + dp[i-1][j]
                dp[i][nj] %= MOD
        else:
            nj = (int(c)*a[i]+j) % 13
            dp[i][nj] = dp[i][nj] + dp[i-1][j]
            dp[i][nj] %= MOD
print(dp[-1][5])

Fixed submission:
from sys import stdin
S = (stdin.readline().rstrip())
dp = [[0]*13 for i in range(len(S)+1)]
MOD = 10**9+7
 
S = list(reversed(S))
dp[0][0] = 1
 
t = 1
for i, c in enumerate(S, 1):
    for j in range(13):
        if c == "?":
            for k in range(10):
                nj = (k*t+j) % 13
                dp[i][nj] = dp[i][nj] + dp[i-1][j]
                dp[i][nj] %= MOD
        else:
            nj = (int(c)*t+j) % 13
            dp[i][nj] = dp[i][nj] + dp[i-1][j]
            dp[i][nj] %= MOD
    t = (t*10)%13
print(dp[-1][5])

Buggy python submission (verdict: Time Limit Exceeded):
from sys import stdin
S = (stdin.readline().rstrip())
dp = [[0]*13 for i in range(len(S)+1)]
MOD = 10**9+7

S = list(reversed(S))
a = [0] + [(10**i) % 13 for i in range(len(S))]
dp[0][0] = 1

cnt = 1
for i, c in enumerate(S, 1):
    for j in range(13):
        if c == "?":
            for k in range(10):
                nj = (k*a[i]+j) % 13
                dp[i][nj] = dp[i][nj] + dp[i-1][j]
                dp[i][nj] %= MOD
        else:
            nj = (int(c)*a[i]+j) % 13
            dp[i][nj] = dp[i][nj] + dp[i-1][j]
            dp[i][nj] %= MOD
print(dp[-1][5])

Fixed submission:
from sys import stdin
S = (stdin.readline().rstrip())
dp = [[0]*13 for i in range(len(S)+1)]
MOD = 10**9+7
 
S = list(reversed(S))
dp[0][0] = 1
 
t = 1
for i, c in enumerate(S, 1):
    for j in range(13):
        if c == "?":
            for k in range(10):
                nj = (k*t+j) % 13
                dp[i][nj] = dp[i][nj] + dp[i-1][j]
                dp[i][nj] %= MOD
        else:
            nj = (int(c)*t+j) % 13
            dp[i][nj] = dp[i][nj] + dp[i-1][j]
            dp[i][nj] %= MOD
    t = (t*10)%13
print(dp[-1][5])