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)

/* Coached by rainboy */
#include <stdio.h>
#include <string.h>

#define N 100000
#define MD 1000000007

int main() {
	static char s[N + 1];
	static int dp[N + 1][13];
	int n, i, r, d;	

	scanf("%s", s);
	n = strlen(s);
	dp[0][0] = 1;
	for (i = 0; i < n; i++)
		for (r = 0; r < 13; r++)
			if (s[i] == '?')
				for (d = 0; d <= 9; d++)
					dp[i + 1][(r * 10 + d) % 13] = (dp[i + 1][(r * 10 + d) % 13] + dp[i][r]) % MD;
			else {
				d = s[i] - '0';
				dp[i + 1][(r * 10 + d) % 13] = (dp[i + 1][(r * 10 + d) % 13] + dp[i][r]) % MD;
			}
	printf("%d\n", dp[n][5]);
	return 0;
}