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.Scanner;


public class Main {

    public static void main(String [] args) {
        Scanner scanner = new Scanner(System.in);
        String s = scanner.next();
        long mod = 1000000007L;
        int n = s.length();
        long [][] number = new long[n + 1][13];
        number[0][0] = 1;
        for (int i = 1; i <= n; ++i) {
            if (s.charAt(i - 1) == '?') {
                for (int j = 0; j <= 9; ++j) {
                    for (int k = 0; k <= 12; ++k) {
                        if (number[i - 1][k] > 0) {
                            int currentMod = ( k * 10 + j  + 13) % 13;
                            number[i][currentMod] += number[i - 1][k];
                            number[i][currentMod] %= mod;
                        }
                    }
                }
            } else {
                int current = s.charAt(i - 1) - '0';
                for (int k = 0; k <= 12; ++k) {
                    int currentMod = ( k * 10 + current  + 13) % 13;
                    number[i][currentMod] += number[i - 1][k];
                    number[i][currentMod] %= mod;
                }
            }

        }
        System.out.println(number[n][5]);

    }
}