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: Runtime Error)

import java.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {

    public static void main(String[] args) throws Exception {
        try (BufferedReader reader = new BufferedReader(new InputStreamReader(System.in))) {
            String S = reader.readLine();

            int MOD = 1000000007;

            long[][] count = new long[10003][13];

            count[0][0] = 1;

            for (int i = 1; i <= S.length(); i++) {
                char c = S.charAt(i - 1);

                if (c != '?') {
                    int j = c - '0';
                    for (int k = 0; k < 13; k++) {
                        count[i][(k * 10 + j) % 13] = count[i - 1][k];
                    }
                } else {
                    for (int j = 0; j < 10; j++) {
                        for (int k = 0; k < 13; k++) {
                            count[i][(k * 10 + j) % 13] += count[i - 1][k];
                        }
                    }

                    for (int k = 0; k < 13; k++) {
                        count[i][k] %= MOD;
                    }
                }
            }

            System.out.println(count[S.length()][5]);
        }
    }

}