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 <string>
#include <cmath>
using namespace std;

int main(){
    int N=13;
    string s;
    cin>>s;
    
    int dp[s.length()+1][N] = {};
    dp[0][0] = 1;

    for(int i=0; i<s.length(); i++){
        char c = s[i];
        for(int j=0; j<N; j++){
            for(int k=0; k<10; k++){
                if(c != '?' && c-'0' != k) continue;
                dp[i+1][(10*j+k)%N] += dp[i][j];
                dp[i+1][(10*j+k)%N] %= 1000000007;
            }
        }
    }

    cout<<dp[s.length()][5]<<endl;
}