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: Wrong Answer)

#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#include <iostream>
typedef long long ll;
using namespace std;


int main() {
  string s;
  cin>>s;
  ll mod=1e9+7,a=1,amari=0;
  ll n=s.size();
  ll dp[100005][13];
  dp[0][0]=1;
  rep(i,12) dp[0][i+1]=0;
  
  for(int i=0; i<n; i++){
    int c=0;
    if(s[i]=='?'){
      c=-1;
    }else{
      c=s[i]-'0';
    }
    for(int j=0; j<10; j++){
      int num=0;
      if(c!=-1&&c!=j)
        continue;
      for(int k=0; k<13; k++){
        num=(k*10+j)%13;
        dp[i+1][num]+=dp[i][k];
      }
      rep(k,13)
        dp[i+1][k]%=mod;
    }
  }
      
   cout<<dp[n][5]<<endl; 
  
}