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: Wrong Answer)

import java.util.*;

public class Main{
    public static void main(String args[]){

        Scanner sc = new Scanner(System.in);
        String str = sc.next();

        int mod = (int)1e9+7;
        char arr[] = str.toCharArray();
        int dp[][] = new int[str.length()][13];

        dp[0][0]=1;

        if (arr[0]=='?'){
            for (int i=1; i<10; i++) dp[0][i]=1;
        }else{
            int t = arr[0]-'0';
            dp[0][t]=1;
        }
//        for (int i=0; i<10; i++) dp[0][i]=1;

        for (int i=1; i<str.length(); i++){
            int x = -1;
            if (arr[i]!='?'){
                x = arr[i] - '0';
            }
            for (int j=0; j<10; j++){
                if (x==-1 || x==j){
                    for (int k=0; k<13; k++){
                        int m = (k*10+j)%13;
                        dp[i][m] += dp[i-1][k];
                        dp[i][m] %= mod;
                    }
                }
            }
        }

        if (arr[0]=='?') System.out.println(dp[str.length()-1][5]);
        else System.out.println(dp[str.length()-1][5]-1);
//        System.out.println(dp[str.length()-1][2]);
//        System.out.println(dp[0][6]);


    }

}