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: Time Limit Exceeded)

def main():
    s=input()
    n=len(s)
    mod=10**9+7
    
    dp=[[0]*13 for _ in range(n)]
    if s[-1]=="?":
        dp[0]=[1,1,1,1,1,1,1,1,1,1,0,0,0]
    else:
        dp[0][int(s[-1])]=1
    
    for i in range(1,n):
        ss=s[n-i-1:n]
    #     print(i,ss)
        ss0=ss[0]
        if ss0!="?":
            dp[i] = [ dp[i-1][(j-int(ss0)*10**i)%13] %mod for j in range(13)]
        else:
            dp[i] = [sum( dp[i-1][(j-k*10**i)%13] for k in range(10)) %mod for j in range(13) ]
    print(dp[-1][5])
    
if __name__ == '__main__':
    main()