Buggy python submission (verdict: Time Limit Exceeded):
def STR(): return input()

mod = 1000000007

s = STR()
l = len(s)
dp = [[0] * 13 for _ in range(l + 1)] #dp[i]i桁目まで決めた時の13で割ったあまりが[j]の個数
dp[0][0] = 1

for i in range(l + 1): #i桁目まで決める
    if s[i-1] == '?':
        for j in range(13): #i-1桁目のあまりがj
            a = dp[i-1][j]
            b = j * 10
            for k in range(10): #i桁目の値
                dp[i][(b + k) % 13] += a
        for j in range(13):
            dp[i][j] %= mod
    else:
        a = int(s[i-1])
        for j in range(13): #i-1桁目のあまりがj
            num = (j * 10 + a) % 13
            dp[i][num] += dp[i-1][j]
            dp[i][num] %= mod
#print(dp)
print(dp[l][5])


Fixed submission:
def STR(): return input()

mod = 1000000007

s = STR()
l = len(s)
dp = [[0] * 13 for _ in range(l + 1)] #dp[i]i桁目まで決めた時の13で割ったあまりが[j]の個数
dp[0][0] = 1


for i in range(l + 1): #i桁目まで決める
    if s[i-1] == '?':
        for j in range(13): #i-1桁目のあまりがj
            a = dp[i-1][j]
            b = j * 10
            for k in range(10): #i桁目の値
                dp[i][(b + k) % 13] += a
        for j in range(13):
            dp[i][j] %= mod
    else:
        a = int(s[i-1])
        for j in range(13): #i-1桁目のあまりがj
            num = (j * 10 + a) % 13
            dp[i][num] += dp[i-1][j]
            dp[i][num] %= mod
#print(dp)
print(dp[l][5])

Buggy python submission (verdict: Time Limit Exceeded):
def STR(): return '?' * pow(10, 5)#input()

mod = 1000000007

s = STR()
l = len(s)
dp = [[0] * 13 for _ in range(l + 1)] #dp[i]i桁目まで決めた時の13で割ったあまりが[j]の個数
dp[0][0] = 1

for i in range(l + 1): #i桁目まで決める
    if s[i-1] == '?':
        for j in range(13): #i-1桁目のあまりがj
            a = dp[i-1][j]
            b = j * 10
            for k in range(10): #i桁目の値
                dp[i][(b + k) % 13] += a
        for j in range(13):
            dp[i][j] %= mod
    else:
        a = int(s[i-1])
        for j in range(13): #i-1桁目のあまりがj
            num = (j * 10 + a) % 13
            dp[i][num] += dp[i-1][j]
            dp[i][num] %= mod
#print(dp)
print(dp[l][5])


Fixed submission:
def STR(): return input()

mod = 1000000007

s = STR()
l = len(s)
dp = [[0] * 13 for _ in range(l + 1)] #dp[i]i桁目まで決めた時の13で割ったあまりが[j]の個数
dp[0][0] = 1


for i in range(l + 1): #i桁目まで決める
    if s[i-1] == '?':
        for j in range(13): #i-1桁目のあまりがj
            a = dp[i-1][j]
            b = j * 10
            for k in range(10): #i桁目の値
                dp[i][(b + k) % 13] += a
        for j in range(13):
            dp[i][j] %= mod
    else:
        a = int(s[i-1])
        for j in range(13): #i-1桁目のあまりがj
            num = (j * 10 + a) % 13
            dp[i][num] += dp[i-1][j]
            dp[i][num] %= mod
#print(dp)
print(dp[l][5])

Buggy python submission (verdict: Time Limit Exceeded):
import sys, re, os
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians
from itertools import permutations, combinations, product, accumulate
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from fractions import gcd

def input(): return sys.stdin.readline().strip()
def STR(): return input()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def S_MAP(): return map(str, input().split())
def LIST(): return list(map(int, input().split()))
def S_LIST(): return list(map(str, input().split()))

sys.setrecursionlimit(10 ** 9)
inf = sys.maxsize
mod = 10 ** 9 + 7

s = STR()
l = len(s)

dp = [[0 for _ in range(13)] for _ in range(l)] #dp[i]i桁目まで決めた時の13で割ったあまりが[j]の個数
if s[0] == '?':
    for i in range(10):
        dp[0][i] = 1
else:
    dp[0][int(s[0])] = 1

for i in range(1, l): #i桁目まで決める
    for j in range(13): #i-1桁目のあまりがj
        if s[i] != '?':
            num = (j * 10 + int(s[i])) % 13
            dp[i][num] += dp[i-1][j]
            dp[i][num] %= mod
        else:
            for k in range(10): #i桁目の値
                num = (j * 10 + k) % 13
                dp[i][num] += dp[i-1][j]
                dp[i][num] %= mod
#print(dp)
print(dp[l-1][5])


Fixed submission:
def STR(): return input()

mod = 1000000007

s = STR()
l = len(s)
dp = [[0] * 13 for _ in range(l + 1)] #dp[i]i桁目まで決めた時の13で割ったあまりが[j]の個数
dp[0][0] = 1


for i in range(l + 1): #i桁目まで決める
    if s[i-1] == '?':
        for j in range(13): #i-1桁目のあまりがj
            a = dp[i-1][j]
            b = j * 10
            for k in range(10): #i桁目の値
                dp[i][(b + k) % 13] += a
        for j in range(13):
            dp[i][j] %= mod
    else:
        a = int(s[i-1])
        for j in range(13): #i-1桁目のあまりがj
            num = (j * 10 + a) % 13
            dp[i][num] += dp[i-1][j]
            dp[i][num] %= mod
#print(dp)
print(dp[l][5])