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 REP(i,x) for(int i=0;i<(int)(x);i++)
#define REPS(i,x) for(int i=1;i<=(int)(x);i++)
#define RREP(i,x) for(int i=((int)(x)-1);i>=0;i--)
#define RREPS(i,x) for(int i=((int)(x));i>0;i--)
#define FOR(i, m, n) for(int i = m;i < n;i++)
#define ALL(v) v.begin(), v.end()
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );
#define IOS ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define INTXT std::ifstream in ("input.txt"); std::cin.rdbuf(in.rdbuf());
#define INF 1e9

using namespace std;
typedef long long ll;
static const int MOD = 1000000007LL;

ll dp[100005][13];

signed main() {
  IOS
  string s;
  cin >> s;
  
  dp[0][0] = 1;

  REP(i, s.size()){
    int l = s.size() - i - 1;
    if (s.at(i) == '?'){
      REP(j, 13){
        REP(k, 10){
          dp[i + 1][(10 * j + k) % 13] += dp[i][j] % MOD;
        }
      }
    }
    else {
      int k = (int)(s.at(i) - '0');
      REP(j, 13){
        dp[i + 1][(10 * j + k) % 13] += dp[i][j] % MOD;
      }
    }
  }
  cout << dp[s.size()][5] % MOD << endl;
}