Problem:
Score : 400 points

Problem Statement

Given is a string S. Each character in S is either a digit (0, ..., 9) or ?.

Among the integers obtained by replacing each occurrence of ? with a digit, how many have a remainder of 5 when divided by 13? An integer may begin with 0.

Since the answer can be enormous, print the count modulo 10^9+7.

Constraints

S is a string consisting of digits (0, ..., 9) and ?.

1 \leq |S| \leq 10^5

Input

Input is given from Standard Input in the following format:

S

Output

Print the number of integers satisfying the condition, modulo 10^9+7.

Sample Input 1

??2??5

Sample Output 1

768

For example, 482305, 002865, and 972665 satisfy the condition.

Sample Input 2

?44

Sample Output 2

1

Only 044 satisfies the condition.

Sample Input 3

7?4

Sample Output 3

0

We may not be able to produce an integer satisfying the condition.

Sample Input 4

?6?42???8??2??06243????9??3???7258??5??7???????774????4?1??17???9?5?70???76???

Sample Output 4

153716888

Solution in PyPy3 (2.4.0) (judge verdict: Accepted)

from copy import deepcopy

S = input()

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

tens_mod = [1, 10, 9, 12, 3, 4]
mod = int(10**9 + 7)

for i, s in enumerate(S[::-1]):
    if s == "?":
        for j in range(13):
            dp[j] = 0
            for k in range(10):
                dp[j] += dp_past[(j - k * tens_mod[i % 6]) % 13]
            dp[j] %= mod

    else:
        k = int(s)
        for j in range(13):
            dp[j] = dp_past[(j - k * tens_mod[i % 6]) % 13]
    dp_past = deepcopy(dp)

print(dp[5] % mod)