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 static System.Console;
using static System.Math;

namespace AtTest.ABC_135
{
    class D
    {
        static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(OpenStandardOutput()) { AutoFlush = false };
            SetOut(sw);

            Method(args);

            Out.Flush();
        }

        static void Method(string[] args)
        {
            string s = Read();
            int[] mods = new int[s.Length];
            mods[0] = 1;
            for(int i = 1; i < s.Length; i++)
            {
                mods[i] = (mods[i - 1] * 10) % 13;
            }
            Array.Reverse(mods);
            long mask = 1000000000 + 7;
            long defaultMod = 0;
            for(int i = 0; i < s.Length; i++)
            {
                if (s[i] == '?') continue;

                defaultMod += mods[i] * (s[i] - '0');
                defaultMod %= 13;
            }
            long[] cnts = new long[13];
            cnts[defaultMod] = 1;
            for(int i = 0; i < s.Length; i++)
            {
                if (s[i] != '?') continue;

                long[] next = new long[13];
                for(int j = 0; j < 10; j++)
                {
                    int delta = mods[i] * j;
                    for(int k = 0; k < 13; k++)
                    {
                        next[(k + delta) % 13] += cnts[k];
                        next[(k + delta) % 13] %= mask;
                    }
                }
                cnts = next;
            }

            WriteLine(cnts[5]);
        }

        private static string Read() { return ReadLine(); }
        private static char[] ReadChars() { return Array.ConvertAll(Read().Split(), a => a[0]); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}