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) throws Exception {
		Scanner sc = new Scanner(System.in);
		char[] s = sc.next().toCharArray();
		sc.close();

		long[][] dp = new long[s.length + 1][13];
		dp[0][0] = 1;
		for (int i = 1; i < dp.length; i++) {
			if (s[i - 1] == '?') {
				for (int j = 0; j < 10; j++) {
					for (int j2 = 0; j2 < 13; j2++) {
						dp[i][(j2 * 10 + j) % 13] += dp[i - 1][j2];
					}
				}
			} else {
				int j = s[i - 1] - '0';
				for (int j2 = 0; j2 < 13; j2++) {
					dp[i][(j2 * 10 + j) % 13] += dp[i - 1][j2];
				}
			}
			for (int j2 = 0; j2 < 13; j2++) {
				dp[i][j2] %= 1000000007;
			}
		}
		System.out.println(dp[s.length][5]);
	}
}