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.PrintStream;
import java.util.Scanner;

public class Main {
	static final PrintStream out = System.out;
	static Scanner sc = new Scanner(System.in);
	static final long Mod = 1000_000_007L;
	public static void main(String[] args) {
		Main main = new Main();
		main.solve();
		System.exit(0);
	}

	void solve() {
		String S = next();
		int N = S.length();
		char[] C = S.toCharArray();
		long[][] dp = new long[100010][15];
		dp[0][0]=1L;

		for(int i=0;i<N;i++) {
			for(int j=0;j<13;j++) {
				for(int k=0;k<=9;k++) {
					if(k==C[i]-'0'||C[i]=='?') {
						dp[i+1][(j*10+k)%13]=(dp[i+1][(j*10+k)%13]+dp[i][j])%Mod;
					}
				}
			}
		}
		out.println(dp[N][5]);
	}

	public int[] nextIntArray(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)a[i] = nextInt();
		return a;
	}
	public long[] nextLongArray(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++)a[i] = nextLong();
		return a;
	}
	public int nextInt() {
		return Integer.parseInt(next());
	}
	public long nextLong() {
		return Long.parseLong(next());
	}
	public String next() {
		return sc.next();
	}
}