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: Wrong Answer)

d=[0]*13
d[0]=1
mul=1
mulmod=1
t=list(input())
t.reverse()
zero=[0]*13
l=len(t)
modlist=[10**i%13 for i in range(l)]
for n,c in enumerate(t):
    e=zero[:]

    for i in (range(10) if c=="?" else[int(c)]):
        for j in range(13):
            #e[(i*mul+j)%13]+=d[j]
            k=(i*modlist[n])%13
            e[k]+=d[j]
            e[k]%=1000000007
    d,e=e,d
    mul*=10
    #mulmod=mul%13
print(d[5])