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 long mod;
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		String S = sc.next();
		long mod = (long)Math.pow(10, 9)+7; 
		final int N = 13; 
		long r[] = new long[N];
		
		r[0]=1;//初期値で、0を13で割った余りは0
		int last = S.length()-1;
		long mul = 1;//見てる桁数
		for(int i=0;i<=last;i++) {
			long nextr[] = new long[N];
			if(S.charAt(last-i)=='?') {
				for(int j=0;j<=9;j++) {
					int tmp =(int)((j*mul)%N);
					for(int k=0;k<N;k++) {
						nextr[(k+tmp)%N] += r[k];
						nextr[(k+tmp)%N] %= mod;
					}
				}
			}else {
				int j = (int)(S.charAt(last-i)-'0');
				int tmp = (int)((j*mul)%N);
				for(int k=0;k<N;k++) {
					nextr[(k+tmp)%N] += r[k];
					nextr[(k+tmp)%N] %= mod;
				}
			}
			mul *= 10;
			mul %= mod;
			r = nextr;		
		}
		long ans = r[5];
		System.out.println(ans);
	}
}