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++ (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <string> 
//#include <bits/stdc++.h>
using namespace std;

int main(){
    string s;
    cin >>s;
    //s=string(100000,'?');
    int n=13;
    long mod=1000*1000*1000+7;
    long *dp=new long[n]() ;
    dp[0]=1;
    int cal[n][10];
    for(int i=0;i<n;i++){
        for(int j=0;j<10;j++){
            cal[i][j]=i*j%13;
        }
    }
    long b=0;
    long mul=1;
    for(int i=s.length()-1;i>=0;i--){
        //cout<<mul%mod<<endl;
        if(char(s[i])!='?'){b+=int(s[i]-'0')*mul%13;}
        else{
            long *tmp_dp = new long[n]();
            for(int j=0;j<n;j++){
                for(int k=0;k<10;k++){
                    tmp_dp[(cal[mul%13][k]+j)%13]+=dp[j]%mod;
                    tmp_dp[(cal[mul%13][k]+j)%13]%=mod;
                }
            }
            //dp=tmp_dp;
           
            
            for(int j=0;j<n;j++){
                //cout<<tmp_dp[j]<<endl;
                dp[j]=tmp_dp[j]%mod;
            }
            

        }

        mul*=10;
    }
    b%=13;
    int ans;
    if (b<=5){ans=5-b;}
    else{ans=18-b;}
    //cout << ans << endl;
    cout << dp[ans]%mod << endl;
    return 0;
}