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<cstring>
#include<algorithm>
#include<vector>
#include<map>
#include<cmath>
#include<string>
#include<bitset>
#include <sstream>
#include<queue>
#include<set>
#define rep(i,n) for(ll i=0;i<(n);++i)
using namespace std;
typedef long long ll;
typedef pair<int,ll>P;

const ll mod = 1e9+7;

int main()
{
    string s;
    cin>>s;
    vector<vector<ll>> dp(100005,vector<ll>(13,0));

    dp[0][0]=1;
    ll len=s.length();

    rep(i,len)
    {
        if(s[i]=='?')
        {
            rep(j,10)
            {
                rep(k,13)
                {
                    dp[i+1][(k*10+j)%13]+=dp[i][k]%=mod;
                }
            }
        }
        else
        {
            rep(k,13)
            {
                dp[i+1][(k*10+(int)(s[i]-'0'))%13]+=dp[i][k];
            }
        }
        rep(j,13)dp[i+1][j]%=mod;
        
    }
    cout<<dp[len][5];
}