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 Java7 (OpenJDK 1.7.0) (judge verdict: Accepted)

import java.util.*;

public class Main {

	static final int r = 1000000000 + 7;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		String s = sc.next();
		sc.close();
		int n = s.length();
		long dp[][] = new long[n + 1][13];
		dp[0][0] = 1;
		for(int i = 0; i < n; ++i) {
			char t = s.charAt(i);
			int c = -1;
			if(t != '?')c = t - '0';
			for(int j = 0; j < 10; ++j) {
				if(c != -1 && c != j) continue;
				for(int k = 0; k < 13; ++k) {
					dp[i + 1][(k * 10 + j) % 13] += dp[i][k];
				}
			}
			for(int j = 0; j < 13; ++j)dp[i + 1][j] %= r;
		}
		long ans = dp[n][5];
		System.out.println(ans);
	}
}