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: Accepted)

import java.util.*;
import java.util.Map.Entry;
 
class Main {
	 static int mod =  (int) (Math.pow(10,9)+7);
//	 static int mod = 998244353;
   public static void main(String[] args) {
	   
       Scanner sc = new Scanner(System.in);
       String  S = sc.next();
       char[] c = S.toCharArray();

       long[][] dp = new long[c.length+15][13];
       
       if(c[c.length-1]=='?') {
    	   for(int i=0;i<10;i++) {
    		   dp[0][i]=1;
    	   }
       } else {
    	   dp[0][Character.getNumericValue(c[c.length-1])]=1;
       }
       
       int amari=1;
       for(int i=1;i<c.length;i++) {
    	   amari=(amari*10)%13;
    	   if(c[c.length-1-i]=='?') {
    		   for(int j=0;j<10;j++) {
    			   for(int k=0;k<13;k++) {
        			   dp[i][(k+j*amari)%13]=(dp[i][(k+j*amari)%13]+dp[i-1][k])%mod;    				   
    			   }
    		   }
    	   } else {
    		   int tmp=Character.getNumericValue(c[c.length-1-i]);
			   for(int k=0;k<13;k++) {
    			   dp[i][(k+tmp*amari)%13]=(dp[i][(k+tmp*amari)%13]+dp[i-1][k])%mod;    				   
			   }
    	   }
       }

       System.out.println(dp[c.length-1][5]);
       
   }
}