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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {
    static final int MODULUS = 1_000_000_007;
    static final int M = 13;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        String S = sc.next();

        System.out.println(solve(S));

        sc.close();
    }

    static int solve(String S) {
        int[] wayNums = new int[M];
        wayNums[0] = 1;

        for (char ch : S.toCharArray()) {
            int[] nextWayNums = new int[M];

            int lower;
            int upper;
            if (ch == '?') {
                lower = 0;
                upper = 9;
            } else {
                lower = ch - '0';
                upper = ch - '0';
            }

            for (int i = 0; i < M; ++i) {
                for (int digit = lower; digit <= upper; ++digit) {
                    int remainder = (i * 10 + digit) % M;
                    nextWayNums[remainder] = addMod(nextWayNums[remainder], wayNums[i]);
                }
            }

            wayNums = nextWayNums;
        }

        return wayNums[5];
    }

    static int addMod(int x, int y) {
        return (x + y) % MODULUS;
    }
}