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 Python (3.4.3) (judge verdict: Wrong Answer)

def main():
    import numpy as np
    s = list(reversed(input()))
    mod = 10**9+7
    memo = np.zeros(13, dtype=np.int32)
    m13 = [(10**i) % 13 for i in range(12)]
    memo[0] = 1
    for i in range(len(s)):
        memo2 = np.zeros(13, dtype=np.int32)
        a = m13[i % 12]
        if s[i] == "?":
            list_ = np.arange(10)
        else:
            list_ = np.array([int(s[i])])
        list_ = a*list_ % 13
        for l in list_:
            memo2[l:] += memo[:13-l]
            memo2[:l] += memo[13-l:]
        memo = memo2 % mod
    print(int(memo[5]))


main()