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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
public class Main {
	public static void main(String[] args) throws IOException {
      
		int mod = (int) 1E9 + 7;
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		char[] s = br.readLine().toCharArray();
		long dp[][] = new long[s.length][13];

		if ( s[0] == '?' ) {
			for ( int n = 0; n < 10; n++ ) {
				dp[0][n] = 1;
			}
		} else {
			dp[0][s[0] - '0'] = 1;
		}

		for ( int i = 1; i < s.length; i++ ) {
			for ( int r = 0; r < 13; r++ ) {
				if ( s[i] != '?' ) {
					int now = s[i] - '0';
					dp[i][(r * 10 + now) % 13] += dp[i - 1][r];
				}
				else {
					for ( int now = 0; now < 10; now++ ) {
						dp[i][(r * 10 + now) % 13] += dp[i - 1][r];
					}
				}
			}

			for ( int t = 0; t < 13; t++ ) {
				dp[i][t] %= mod;
			}
		}
		System.out.println(dp[s.length - 1][5]);
		br.close();
	}
}