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)

// D.

#include <iostream>
#include <sstream>
#include <algorithm>
#include <vector>

using namespace std;

typedef long long LL;
const LL MOD = 1000000007;

int main(int argc, char *argv[]) {
	string s;
	cin >> s;
	int len = (int)s.length();
	vector<vector<LL>> dp(len + 1, vector<LL>(13));
	for (int j = 0; j < 10; ++j) {
		dp[0][0] = 1;
	}
	LL r = 1;
	for (int i = 0; i < len; ++i) {
		int col = len - i - 1;
		if (s[col] == '?') {
			for (int d = 0; d < 10; ++d) {
				LL v = r * d;
				for (int j = 0; j < 13; ++j) {
					LL w = (v + j) % 13;
					dp[i + 1][w] = (dp[i + 1][w] + dp[i][j]) % MOD;
				}
			}
		} else {
			LL d = s[col] - '0';
			LL v = r * d;
			for (int j = 0; j < 13; ++j) {
				LL w = (v + j) % 13;
				dp[i + 1][w] = (dp[i + 1][w] + dp[i][j]) % MOD;
			}
		}
		r = (r * 10) % 13;
	}
	LL ans = dp[len][5];
	cout << ans << endl;
	return 0;
}