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>
#define mod 1000000007
using namespace std;

typedef long long ll;
ll dp[100006][13];
int main()
{
    
    string s;
    cin>>s;
    for(int i=0;i<=s.size();i++) for(int j=0;j<13;j++) dp[i][j]=0;
    dp[0][0]=1;
    for(int i=0;i<s.size();i++){
        for(int j=0;j<13;j++){
            if(dp[i][j]!=0) {
                if(s[i]=='?'){
                    for(int x=0;x<=9;x++){ dp[i+1][((10*j)+x)%13]+=dp[i][j]%mod; dp[i+1][((10*j)+x)%13]%=mod; }
                }
                else {
                    ll val= (10*j)+s[i]-'0'; val%=13;
                    dp[i+1][val]+=dp[i][j]; dp[i+1][val]%=mod;
                }
            }
        }
    }
    cout<<dp[s.size()][5]%mod<<endl;
    
}