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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <cstdio>
#define N 100005
using namespace std;

typedef long long ll;
ll M = 1e9 + 7;
ll m = 13, d[N][15];
string s;
int main()
{
	int i, j, k, t = 1;
	cin >> s;
	d[s.size()][0] = 1;
	for (i = s.size() - 1; i >= 0; i--, t = t * 10 % m) {
		if (s[i] == '?') {
			for (j = 0; j <= 9; j++) {
				for (k = 0; k < 13; k++) {
					d[i][(k + j * t) % m] = (d[i][(k + j * t) % m] + d[i + 1][k]) % M;
				}
			}
		} else {
			for (j = 0; j < 13; j++)
				d[i][(j + t * (s[i] - '0')) % m] = (d[i][(j + t * (s[i] - '0')) % m] + d[i + 1][j]) % M;
		}
	}
    cout << d[0][5] << endl;
    return 0;
}