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: Time Limit Exceeded)

def main():
    MOD = 10 ** 9 + 7
    S = input()
    u = [1] + [0] * 12
    v = [0] * 13
    m = 1
    shift = 0
    for s in reversed(S):
        if s == '?':
            for j in range(13):
                v[j] = sum(u[(j - (m * i) % 13) % 13] for i in range(10)) % MOD
            u, v = v, u
        else:
            shift = (shift + m * int(s)) % 13
        m = m * 10 % 13
    return u[(5 - shift) % 13]

print(main())