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)

S = input()
M = 10**9+7

case = [1] + [0] * 12
temp = [0] * 13
unit = 1
before = 0
for i in reversed(range(len(S))):
    if(S[i] == '?'):
        for k in range(13):
            for j in range(10):
                before = (k - unit * j) % 13
                temp[k] += case[before]
            temp[k] %= M
    else:
        for k in range(13):
            before = (k - unit * int(S[i])) % 13
            temp[k] = case[before]
    case = temp
    unit *= 10
    unit %= 13
    temp = [0] * 13

print(case[5])