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

void copy_arr(long a[], long b[], int n)
{
    for (int i = 0; i < n; i++) {
        a[i] = b[i];
    }
}

int main(void)
{
    char s[100001];
    scanf("%s", s);
    long remainder[13] = { 1 };
    long figure_position = 1;
    int num_of_digits = strlen(s);
    const int mod = 1000000007;

    for (int i = num_of_digits - 1; i >= 0; i--) {
        long next_reminder[13] = { 0 };
        if (s[i] == '?') {
            for (int j = 0; j < 10; j++) {
                for (int k = 0; k < 13; k++) {
                    next_reminder[(j * figure_position + k) % 13] += remainder[k];
                    next_reminder[(j * figure_position + k) % 13] %= mod;
                }
            }
        } else {
            int j = s[i] - '0';
            for (int k = 0; k < 13; k++) {
                next_reminder[(j * figure_position + k) % 13] += remainder[k];
                next_reminder[(j * figure_position + k) % 13] %= mod;
            }
        }
        figure_position *= 10;
        figure_position %= 13;
        copy_arr(remainder, next_reminder, 13);
    }

    printf("%ld\n", remainder[5]);

    return 0;
}