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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using System.Collections;

static class Extensions
{
    public static int ToInt(this string s) => int.Parse(s);
    public static long ToLong(this string s) => long.Parse(s);
    public static char ToChar(this string s) => char.Parse(s);
    public static double ToDouble(this string s) => double.Parse(s);
    public static int[] ToIntArray(this string s) => s.Replace(',', ' ').Split(' ').Select(x => x.ToInt()).ToArray();
    public static long[] ToLongArray(this string s) => s.Replace(',', ' ').Split(' ').Select(x => x.ToLong()).ToArray();
    public static double[] ToDoubleArray(this string s) => s.Replace(',', ' ').Split(' ').Select(x => x.ToDouble()).ToArray();
    public static Queue<T> ToQueue<T>(this IEnumerable<T> seq) => new Queue<T>(seq);
    public static Stack<T> ToStack<T>(this IEnumerable<T> seq) => new Stack<T>(seq);
    public static HashSet<T> ToHashSet<T>(this IEnumerable<T> seq) => new HashSet<T>(seq);
}
static class MyMath
{
    static public long GCD(long a, long b) => (a < b) ? GCD(b, a) : ((b == 0) ? a : GCD(b, a % b));
    static public long LCM(long a, long b) => (a > b) ? (a / GCD(a, b) * b) : (b / GCD(a, b) * a);
    static private readonly long _m = 1000000000 + 7;
    static public long Mod(long val) => (val % _m + _m) % _m;
    static private long ExtGCD(long a, long b, ref long x, ref long y) => (b == 0) ? (a + (x = 1) * 0 + (y = 0) * 0) : (ExtGCD(b, a % b, ref y, ref x) + (y -= a / b * x) * 0);
    static private long ModInverseInner(long a, long dummy1 = 0, long dummy2 = 0) => ExtGCD(a, _m, ref dummy1, ref dummy2) * 0 + Mod(dummy1);
    static public long ModInverse(long a) => ModInverseInner(a, 0, 0);
}

class Program
{
    static string[] ReadLines(int n) => Enumerable.Range(0, n).Select(s => Console.ReadLine()).ToArray();

    static void Main()
    {
        string s = Console.ReadLine();

        long[] dp = new long[13];
        dp[0] = 1;
        int keta = 1;
        
        for(int i = s.Length - 1; i >= 0; i--)
        {
            long[] nextDP = new long[13];

            if (s[i] == '?')
            {
                for (int j = 0; j <= 9; j++)
                {
                    int amari = (j * keta) % 13;
                    for (int k = 0; k < 13; k++)
                    {
                        nextDP[(k + amari) % 13] += MyMath.Mod(dp[k]);
                        nextDP[(k + amari) % 13] = MyMath.Mod(nextDP[(k + amari) % 13]);
                    }
                }
            }
            else
            {
                int val = int.Parse(s[i].ToString());
                int amari = (val * keta) % 13;
                for(int j = 0; j < 13; j++)
                {
                    nextDP[(j + amari) % 13] = MyMath.Mod(dp[j]);
                }
            }

            keta *= 10;
            keta %= 13;

            dp = nextDP;
        }

        Console.WriteLine(dp[5]);
    }
    
}