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.math.BigInteger;
import java.util.ArrayList;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		
		Scanner sc = new Scanner(System.in);
		String s = sc.next();
		
		s.toCharArray();
		int keta = s.length();
		int[][] keta_amari = new int [keta][13];
		if (s.charAt(keta-1) == '?') {
			for (int i = 0 ; i < 9; i ++) {
				keta_amari[0][i] ++;
			}
		}else {
			//System.out.println(Character.getNumericValue(s.charAt(keta -1)));
			keta_amari[0][Character.getNumericValue(s.charAt(keta -1))%13] ++;
		}
		
		for (int k = 2 ; k <=keta ; k ++) {
			if(s.charAt(keta -k) != '?') {
				int l  = Character.getNumericValue(s.charAt(keta -k)); 
				int temp = (int) ((l*Math.pow(10, k-1))%13);
				for (int i = 0 ; i < 13 ;i ++) {
					keta_amari[k-1][i] = keta_amari[k-2][((13-temp) +i)%13];
					//System.out.println(((13-temp) +i)%13);
				}
			}else {
				int list[] = {0,1,2,3,4,5,6,7,8,9};
				for (int l: list) {
					int temp = (int) ((l*Math.pow(10, k-1))%13);
					for (int i = 0 ; i < 13 ;i ++) {
						keta_amari[k-1][i] += keta_amari[k-2][((13-temp) +i)%13];
						//System.out.println(((13-temp) +i)%13);
					}	
				}
			}
		}
		
		System.out.println((keta_amari[keta-1][5])%1000000007);	
	}
}