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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <string.h>
#include<stdlib.h>

int main()
{

    char s[100009];

    scanf("%s",s);

    int i,j;

    int len = strlen(s);

    long long p[13];

    p[0] = 1;


    int c = 0;

    long long int a[13];

    int si;

    for(si=0;si<len;si++)
    {

        for(i=0;i<13;i++)
            a[i] = 0;

        if(s[si] =='?')
        {
            for(j=0;j<10;j++)
                for(i=0;i<13;i++)
                    a[(i*10+j)%13] += p[i];
        }
        else
        {
            c = s[si] - '0';
            for(i=0;i<13;i++)
                a[(i*10+c)%13] += p[i];
        }

        
        for(i=0;i<13;i++)
            p[i] = a[i]%1000000007;
        
    }

    printf("%lld",p[5]);

    return 0;
}