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)

s=input()

#i桁以下の数字でmodがjの数
#dp[i][j]=

dp=[[0]*13 for _ in range(len(s))]

MOD=10**9+7

result=0
for i in range(len(s)):
    index=len(s)-i-1

    if i==0:
        if s[index]!="?":
            #数字,300のmodをtempに
            temp=(int(s[index])*(10**i))%13
            dp[index][temp]=1
        else:
            for l in range(10):
                temp=(l*(10**i))%13
                for j in range(13):
                    k=(temp+j)%13
                    dp[index][k]+=1

    else:
        if s[index]!="?":
            #数字,300のmodをtempに
            temp=(int(s[index])*(10**i))%13
            for j in range(13):
                k=(temp+j)%13
                dp[index][k]+=dp[index+1][j]%MOD
        else:
            for l in range(10):
                temp=(l*(10**i))%13
                for j in range(13):
                    k=(temp+j)%13
                    dp[index][k]+=dp[index+1][j]%MOD
    #print(dp[index],sum(dp[index]))



print(dp[0][5]%MOD)