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 (Clang 3.8.0) (judge verdict: Accepted)

# include <cmath>
# include <iostream>
# include <queue>
# include <set>
# include <stack>
# include <string>
# include <vector>


using namespace std;


const int N = 13;
const int MOD = 1e9+7;
const int REM = 5;


int main() {
    string s; cin >> s;
    int n_digits = s.size();

    vector<vector<long>> dp(n_digits+1, vector<long>(13, 0));
    dp[0][0] = 1;

    int c;
    for (int i=0; i<n_digits; i++) {
        c = (s[i] == '?') ? -1 : s[i]-'0';

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

        else {
            for (int k=0; k<13; k++) {
                dp[i+1][(k*10+c)%N] += dp[i][k];
            }
        }

        for (int k=0; k<13; k++) {
            dp[i+1][k] %= MOD;
        }
    }

    cout << dp[n_digits][REM] << endl;
}