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.*;

public class Main {
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        String str = sc.nextLine();
        int len = str.length();
        long mod = (int)Math.pow(10,9)+7;
        long[][] dp = new long[(int)(Math.pow(10, 5))+1][13];
        for(int i=0; i<13; i++) {
            dp[0][i] = 0;
        }
        dp[0][0] = 1;
        int cnt = 0;
        long total = 1;
        
        for(int i=0; i<len; i++) {
            char s = str.charAt(i);
            if(s == '?') {
                for(int j=0; j<13; j++) {
                    dp[i+1][j] = (total+mod*10-dp[i][4-(int)((j+2)/3)]-dp[i][8-(int)((j+1)/3)]-dp[i][12-(int)(j/3)])%mod;
                }
                total = (total*10)%mod;
            } else {
                for(int j=0; j<13; j++) {
                    dp[i+1][j] = 0;
                }
                for(int j=0; j<13; j++) {
                    dp[i+1][(j*10+Character.getNumericValue(s))%13] += dp[i][j];
                }
            }
        }
        System.out.println(dp[len][5]%mod);
        sc.close();
    }
}