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.Threading.Tasks;

namespace ConsoleApp2
{
    using System;
    using System.Linq;

    using Match = System.Int32;

    class Program
    {
        static readonly long DIVIDE_BASE = 1000000007;
        static readonly int REMAINDER_BASE = 13;
        static void Main(string[] args)
        {
            // スペース区切りの整数の入力
            char[] inputs = Console.ReadLine().ToCharArray();
            int n = inputs.Count();
            // 剰余の結果がいくつになる可能性があるかを保存する
            long[] remainderPossibilities = new long[REMAINDER_BASE];
            remainderPossibilities[0] = 1;
            for (int i = 0; i < n; i++)
            {
                long[] newList = new long[REMAINDER_BASE];
                if (inputs[i] == '?')
                {
                    for(int j = 0; j < 10; j++)
                    {
                        long[] tmpList = getNewPossibilitiesByShift(remainderPossibilities, j);
                        newList = VectorSum(newList, tmpList);
                    }
                }
                else
                {
                    int digit = int.Parse(inputs[i].ToString());
                    newList = getNewPossibilitiesByShift(remainderPossibilities, digit);
                }
                remainderPossibilities = newList;
                // Console.WriteLine(string.Join(" ", remainderPossibilities));
            }
            Console.WriteLine(remainderPossibilities[5].ToString());
        }

        static long[] getNewPossibilitiesByShift(long[] oldList, int shiftValue)
        {
            long[] newList = new long[REMAINDER_BASE];
            for (int i = 0; i < REMAINDER_BASE; i++)
            {
                newList[Destination(i, shiftValue)] = (newList[Destination(i, shiftValue)] + oldList[i]) % DIVIDE_BASE;
            }
            return newList;
        }

        static int Destination(int tmp, int shift)
        {
            return (tmp * 10 + shift) % REMAINDER_BASE;
        }

        static long[] VectorSum(long[] vector1, long[] vector2)
        {
            long[] result = new long[REMAINDER_BASE];
            for (int i = 0; i < REMAINDER_BASE; i++)
            {
                result[i] = (vector1[i] + vector2[i]) % DIVIDE_BASE;
            }
            return result;
        }
    }
}