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 <iostream>
#include <cstdio>
#include <cstdlib>
#include <string>
#include <cstring>
#include <cstdint>
using namespace std;
static const long long MOD = 1000000007LL;
#define REP(i,n) for(int i = 0; i < (int)(n); i++)

int main(){
  char c;
  int mod = 1000000007;
  int d[13] = {1};
  while(cin >> c){
    int e[13] = {0};
    REP(i, 13){
      REP(j, 10) if(c == '?' || c == '0' + j){
        (e[(i * 10 + j) % 13] += d[i]) %= mod;
      }
    }
   // REP(i, 13){
   //   d[i] = e[i];
   // }
    d[5]=e[5];
  }
  cout << d[5] << endl;
  return 0;
}