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.*;

public class Main {
    static final int MOD = 1000000007;
	public static void main (String[] args) {
		Scanner sc = new Scanner(System.in);
		char[] arr = sc.next().toCharArray();
		int length = arr.length;
		int[][] dp = new int[length + 1][13];
		dp[0][0] = 1;
		for (int i = 1; i <= length; i++) {
		    for (int j = 0; j < 13; j++) {
		        for (int k = 0; k < 10; k++) {
		            if (arr[i - 1] == '?' || arr[i - 1] - '0' == k) {
		                int idx = (j * 10 + k) % 13;
		                dp[i][idx] += dp[i - 1][j];
		                dp[i][idx] %= MOD;
		            }
		        }
		    }
		}
		System.out.println(dp[length][5]);
   }
}