Buggy python submission (verdict: Time Limit Exceeded):
s = input()
n = len(s)
mod = 10 ** 9 + 7
amari = [1]
for i in range(n - 1):
    amari.append(amari[-1] * 10 % 13)
amari.reverse()
dp = [[0 for i in range(13)] for j in range(n + 1)]
dp[0][0] = 1
for i in range(n):
    for j in range(13):
        if s[i] == "?":
            temp = 0
            for k in range(10):
                temp += dp[i][(j - amari[i] * k) % 13]
                temp %= mod
            dp[i + 1][j] = temp
        else:
            num = int(s[i])
            dp[i + 1][j] = dp[i][(j - amari[i] * num) % 13]
print(dp[n][5])

Fixed submission:
s = input()
n = len(s)
mod = 10 ** 9 + 7
amari = [1]
for i in range(n - 1):
    amari.append(amari[-1] * 10 % 13)
amari.reverse()
dp = [[0 for i in range(13)] for j in range(n + 1)]
dp[0][0] = 1
for i in range(n):
    for j in range(13):
        if s[i] == "?":
            temp = 0
            for k in range(10):
                temp += dp[i][(j - amari[i] * k) % 13]
                temp %= mod
            dp[i + 1][j] = temp
        else:
            num = int(s[i])
            dp[i + 1][j] = dp[i][(j - amari[i] * num) % 13]
print(dp[n][5])

Buggy python submission (verdict: Time Limit Exceeded):
s = input()
mod = 10 ** 9 + 7
dp = []
for i in range(13):
    temp = [0] * len(s)
    dp.append(temp)
amari_list = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]
for i in range(len(s)):
    amari_list.append([10 * amari_list[-1][i] for i in range(10)])
# j桁目がxのとき13で割ったあまり
def amari(x, j):
    if x != "?":
        x = int(x)
        return [amari_list[j][x]]
    else:
        return amari_list[j]
for i in amari(s[-1], 0):
    dp[i][0] = 1
for i in range(1, len(s)):
    for j in range(13):
        for k in amari(s[-i-1], i):
            dp[j][i] += dp[(j - k) % 13][i - 1]
            dp[j][i] %= mod
print(dp[5][len(s) - 1])

Fixed submission:
s = input()
n = len(s)
mod = 10 ** 9 + 7
amari = [1]
for i in range(n - 1):
    amari.append(amari[-1] * 10 % 13)
amari.reverse()
dp = [[0 for i in range(13)] for j in range(n + 1)]
dp[0][0] = 1
for i in range(n):
    for j in range(13):
        if s[i] == "?":
            temp = 0
            for k in range(10):
                temp += dp[i][(j - amari[i] * k) % 13]
                temp %= mod
            dp[i + 1][j] = temp
        else:
            num = int(s[i])
            dp[i + 1][j] = dp[i][(j - amari[i] * num) % 13]
print(dp[n][5])

Buggy python submission (verdict: Time Limit Exceeded):
s = input()
mod = 10 ** 9 + 7
dp = []
for i in range(13):
    temp = [0] * len(s)
    dp.append(temp)
# j桁目がxのとき13で割ったあまり
def amari(x, j):
    if x != "?":
        x = int(x)
        return [(10 ** j % 13) * x]
    else:
        return [(10 ** j % 13) * x for x in range(10)]
for i in amari(s[-1], 0):
    dp[i][0] = 1
for i in range(1, len(s)):
    for j in range(13):
        for k in amari(s[-i-1], i):
            dp[j][i] += dp[(j - k) % 13][i - 1]
            dp[j][i] %= mod
print(dp[5][len(s) - 1])

Fixed submission:
s = input()
n = len(s)
mod = 10 ** 9 + 7
amari = [1]
for i in range(n - 1):
    amari.append(amari[-1] * 10 % 13)
amari.reverse()
dp = [[0 for i in range(13)] for j in range(n + 1)]
dp[0][0] = 1
for i in range(n):
    for j in range(13):
        if s[i] == "?":
            temp = 0
            for k in range(10):
                temp += dp[i][(j - amari[i] * k) % 13]
                temp %= mod
            dp[i + 1][j] = temp
        else:
            num = int(s[i])
            dp[i + 1][j] = dp[i][(j - amari[i] * num) % 13]
print(dp[n][5])