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 <vector>
#include <algorithm>
#include <string>
#include <math.h>

using namespace std;


int main() {

	string S;
	cin >> S;


	vector<vector<int>> dp(100005, vector<int>(13,0));

	int N = S.size();

	vector<int> m(N, 0);

	for (int j = 0; j < N; j++) {
		if (S[j] == '?') {
			m[j] = -1;
		}
		else {
			m[j] = S[j] - '0';
		}

		
	}


	for (int i = 0; i < 10; i++) {
		if (m[0] == -1 || m[0] == i) {
			dp[0][i] = 1;
		}
	}

	for (int i = 1; i < N; i++) {
		for (int j = 0; j < 10; j++) {

			if (m[i] != -1 && m[i] != j) continue;

			for (int k = 0; k < 13; k++) {
				dp[i][(10 * k + j) % 13] += dp[i - 1][k];
				dp[i][(10 * k + j) % 13] %= 1000000007;
			}
		}
		for (int k = 0; k < 13; k++) {
			
		}
	}

	cout << dp[N - 1][5] << endl;

	

	


}