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.util.ArrayList;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		
		Scanner sc = new Scanner(System.in);
		String s = sc.next();
		
		s.toCharArray();
		
		long number = 0;
		int keta = s.length();
		
		
		ArrayList<Integer> ks = new ArrayList<>();
		
		//まずは初期でNONはてなのやつを格納しておく
		for (int k = 0; k < keta ; k ++) {
			if (s.charAt(k) != '?') {		
				ks.add(k);
			}
		};
		int hatena = s.length() -ks.size();
		String st = "";
		long count = 0;
		for (int i = 0 ; i < Math.pow(10, hatena) ; i ++) {
			
			//000001 みたく強制的に文字列にする。
			
			st = new String(i+"");
			if (st.length() < hatena) {
				while (st.length() < hatena) {	
					st = "0" + st;
				}
			}
			StringBuilder sb = new StringBuilder(st);
			for (int j : ks) {	
				sb = sb.insert(j, ""+s.charAt(j));
			}
			if ( Integer.valueOf(new String(sb))% 13 ==5) {		
				count ++;
			}
		}
		System.out.println(count%(10000007));
	}
}