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.Linq;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;
namespace AtCoder_Beginner_Contest_135
{
    class Program
    {
        static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
        static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }
        static void Main(string[] args)
        {
            SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
            Solve();
            Out.Flush();
        }
        static void Solve()
        {
            var S = ReadLine();
            var Si = new long[S.Length];
            var xor10 = new long[S.Length];
            var mod = 13L;
            long Mod = 1000000000 + 7;
            //10^n%13
            xor10[0] = 1;
            for (var i = 1; i < S.Length; ++i)
            { xor10[i] = xor10[i - 1] * 10 % mod; }
            var numxor = 0L;//?が0のときのmod
            var cnt = 0L;
            for (var i = S.Length - 1; 0 <= i; --i) 
            {
                if ('?' != S[i])
                {
                    var n = long.Parse(S[i].ToString());
                    numxor += xor10[cnt] * n;
                    numxor %= mod;
                }
                ++cnt;
            }
            var dp = new long[S.Length + 1, mod];
            for (var i = 1; i <= S.Length; ++i)
            {
                if ('?' != S[i - 1])//?ではない場合そのまま遷移
                {
                    for (var k = 0; k < mod; ++k)
                    {
                        dp[i, k] = dp[i - 1, k];
                    }
                    continue;
                }
                var tmp = new long[mod];
                //i*10^n%modを計算。0は除く
                for (var j = 1; j < 10; ++j)
                {
                    var num = (xor10[S.Length - i] * j) % mod;
                    tmp[num]++;
                }
                //0じゃない場合遷移
                for (var j = 0; j < mod; ++j)
                {
                    //i=0の場合は前のをそのまま加える
                    dp[i, j] += dp[i - 1, j];
                    for (var k = 0; k < mod; ++k)
                    {
                        dp[i, (j + k) % mod] += dp[i - 1, j] * tmp[k];
                    }
                }
                //0から遷移する場合
                for (var j = 0; j < mod; ++j)
                {
                    dp[i, j] += tmp[j];
                    dp[i, j] %= Mod;
                }
            }
            dp[S.Length, 0]++;//全て0の場合;
            WriteLine(dp[S.Length, (5 - numxor + mod) % mod] % Mod);
        }
    }
}