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);
		String s=sc.next();
		long mod=1000000007;
		long[][] dp=new long[s.length()+1][13];
		dp[0][0]=1;
		int rt=1;
		for(int i=1; i<=s.length(); i++){
			if(i!=1){
				rt*=10;
				rt%=13;
			}
			if(s.charAt(s.length()-i)=='?'){
				for(int j=0; j<10; j++){
					for(int u=0; u<13; u++){
						int c=(j*rt)%13;
						dp[i][(c+u)%13]=(dp[i][(c+u)%13]+dp[i-1][u])%mod;
					}
				}
			}else{
				int k=s.charAt(s.length()-i)-'0';
				k*=rt;
				k%=13;
				for(int j=0; j<13; j++){
					dp[i][(j+k)%13]=(dp[i-1][j])%mod;
				}
			}
		}
		System.out.println(dp[s.length()][5]);
	}
}