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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;
import java.util.regex.Pattern;
import java.util.regex.Matcher;

public class Main{
    
    public static void main (String[] args){
        
        Scanner sc = new Scanner (System.in);
        String s = sc.next();
        int num = s.length();
        char [] list = new char [num];
        
        for (int index=0; index<num; index++){
            list[index]=s.charAt(index);
        }
        
        for (int index=0; index<num; index++){
            if (s.charAt(index)=='?'){
               list[index]='.';
            } 
        }
        
        StringBuilder sb = new StringBuilder ();
        
        for (int index=0; index<num; index++){
            
            sb.append(list[index]);
            
        }
     
        Pattern p = Pattern.compile(sb.toString());
        int count = 0;
        
        for (int index=0; ; index++){
            int multiple = index*13+5;
            StringBuilder sb2 = new StringBuilder (String.valueOf(multiple));
            for (; sb2.length()<sb.length();){
                sb2.append('0');
            }
            if (sb2.length()>(sb.length())){
                break;
            }
            Matcher m = p.matcher(sb2);
            
            if (m.find()){
                count++;
            }
        }
        
        System.out.println(count);
        
        
        
    }
}