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 <stdlib.h>
#include <string>
#include <algorithm>
#define llint long long
#define mod 1000000007

using namespace std;

string s;
llint dp[100005][13];

int main(void)
{
	cin >> s;
	int n = s.size();
	reverse(s.begin(), s.end());
	s = "#" + s;
	
	for(int i = 0; i <= n; i++){
		for(int j = 0; j < 13; j++){
			dp[i][j] = 0;
		}
	}
	dp[0][0] = 1;
	
	llint mul = 1;
	for(int i = 0; i < n; i++){
		for(int j = 0; j < 13; j++){
			for(int k = 0; k < 10; k++){
				if(s[i+1] != '?' && s[i+1]-'0' != k) continue;
				(dp[i+1][(j+mul*k)%13] += dp[i][j]) %= mod;
			}
		}
		mul *= 10, mul %= 13;
	}
	cout << dp[n][5] << endl;
	
	return 0;
}