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)

s = input()
S = []
for v in s:
    if v == '?':
        pass
    else:
        v = int(v)
    S.append(v)
length = len(S)

A = [0] * 13
B = [0] * 13
mod = 5
first = 0

for i in range(length):
    a = S[length - i- 1]
    if a != '?':
        a = (a * 10 ** i) % 13
        mod -= a
        mod %= 13
    
    elif first == 0:
        for j in range(10):
            a = (j * 10 ** i) % 13
            A[a] += 1
        first = 1

    else:
        r = (10 ** i) % 13
        for j in range(10):
            a = (j * r) % 13
            for k in range(13):
                B[(k + a) % 13] += A[k]
                B[(k + a) % 13] %= 10 ** 9 + 7
        A = B
        B = [0] * 13


print(A[mod])