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>
int main()
{
	char s[100005];
	scanf("%s", s);
	long long int p = 1000000007;
	long long int i, j, k, n = strlen(s);
	long long int amari[2][13];
	for (i = 0; i < 13; i++)
		amari[0][i] = 0;
	if (s[0] == '?')
		for (i = 0; i < 10; i++)
			amari[0][i] = 1;
	else
		amari[0][s[0] - '0'] = 1;
	for (i = 1; i < n; i++)
	{
		for (j = 0; j < 13; j++)
			amari[1][j] = 0;
		if (s[i] == '?')
		{
			for (j = 0; j < 10; j++)
				for (k = 0; k < 13; k++)
					amari[1][(10 * k + j) % 13] += amari[0][k];
		}
		else
		{
			for (j = 0; j < 13; j++)
				amari[1][(10 * j + (s[i] - '0')) % 13] += amari[0][j];
		}
		for (j = 0; j < 13; j++)
			amari[1][j] %= p;
		for (j = 0; j < 13; j++)
			amari[0][j] = amari[1][j];
	}
	printf("%lld\n", amari[0][5]);
	return 0;
}