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 sc = new Scanner(System.in);
		char[] s = sc.nextLine().toCharArray();
		int[][] dp = new int[s.length + 1][13];

		int m = 1_000_000_007;

		dp[0][0] = 1;
		for (int i = 0; i < s.length; i++) {
			int a = (s[i] == '?') ? -1 : s[i] - '0';
			for (int j = 0; j < 10; j++) {
				if (a != -1 && a != j) continue;
				for (int k = 0; k < 13; k++) {
					dp[i + 1][(k * 10 + j) % 13] = (dp[i + 1][(k * 10 + j) % 13] + dp[i][k]) % m;
				}
			}
		}

		//for (int i = 0; i < dp.length; i++) {
		//	for (int j = 0; j < 13; j++) {
		//		System.out.print(dp[i][j]);
		//		System.out.print(" ");
		//	}
		//	System.out.println();
		//}
		System.out.println(dp[s.length][5]);
	}
}