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)

import sys
input = sys.stdin.readline
def main():  
    S = list(input())
    S.pop()
    length=len(S)
    dp = [0]*13
    dp[0]=1
    mul=1
    mod=1000000007
    for i in range(1,length+1):
        next_dp = [0]*13
        for j in range(13):
            if S[length-i] == "?":
                for k in range(10):
                    j_sub=(j+k*mul)%13
                    next_dp[j_sub]+=dp[j]
                    next_dp[j_sub]%=mod
            else:
                j_sub=(j+int(S[length-i])*mul)%13
                next_dp[j_sub]+=dp[j]
                next_dp[j_sub]%=mod
        dp=next_dp
        mul=mul*10%13
    print(dp[5]%1000000007)
if __name__ == "__main__":
    main()