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: Runtime Error)

#include<bits/stdc++.h>
using namespace std;
const int maxn=1e5+10;
const int mod=1e9+7;
typedef long long LL;
int n,m;
string str;
int dp[maxn][13];

int main()
{
    cin>>str;
    reverse(str.begin(),str.end());
    int n=str.length();
    dp[0][0]=1;
    for(int i=0;i<n-1;i++)
    {
        if(str[i]=='?')
            for(int j=0;i<13;j++)
                for(int k=0;k<10;k++)
                {
                    int id=(j*10+k)%13;
                    dp[i+1][id]=(1LL*dp[i+1][id]+dp[i][j])%mod;
                }
        else
        {
            int k=str[i]-'0';
            for(int j=0;j<13;j++)
            {
                int id=(j*10+k)%13;
                dp[i+1][id]=(1LL*dp[i+1][id]+dp[i][j])%mod;
            }
        }
        
    }
    cout<<dp[n-1][5]<<endl;
}