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<bits/stdc++.h>
using namespace std;
int main(){
    // data loader
    string s;
    cin>>s;
    
    //main
    long long n=s.length();
    long long dp[100005][13]={0};
    dp[0][0]=1;
    for (int i=0;i<n;i++){
        int c;
        if (s[i]=='?'){
            c=-1;
        }else{
            c=s[i]-'0';
        }
        for (int j=0;j<10;j++){
            if (c==-1 || c==j){
                for (int k=0;k<13;k++){
                    dp[i+1][(k*10+j)%13]+=dp[i][k];
                }
            }
        }
        for (int j=0;j<13;j++){
            dp[i+1][j]%=1000000007;
        }
    }
    cout<<dp[n][5]<<endl;
}