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()
n=len(s)
ten=[1]
p=1
mod=10**9+7
for i in range(n-1):
    p*=10
    p%=13
    ten.append(p)
ten=ten[::-1]
dp=[0]*13
dp[0]=1
for t,c in zip(ten,s):
    newdp=[0]*13
    if c!='?':
        c=t*int(c)%13
        for i in range(13):
            newdp[(i+c)%13]=dp[i]
    else:
        for c in range(10):
            c*=t
            for i in range(13):
                newdp[(i+c)%13]+=dp[i]
                newdp[(i+c)%13]%=mod
    dp=newdp

print(newdp[5])