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>

using namespace std;

using ll = long long;
using vi = vector<int>;
using vll = vector<ll>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<ll>>;

ll P = 1000000007;
ll dp[101010][13] = {0};

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  string s;
  cin >> s;
  int n = s.size();
  int po10[101010] = {0};
  po10[0] = 1;
  for (int i = 0; i <= n; i++) po10[i + 1] = (po10[i] * 10) % 13;

  reverse(s.begin(), s.end());
  dp[0][0] = 1;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < 13; j++) {
      if (s[i] == '?') {
        for (int k = 0; k < 10; k++) {
          dp[i + 1][(j + k * po10[i]) % 13] += dp[i][j];
          dp[i + 1][(j + k * po10[i]) % 13] %= P;
        }
      } else {
        dp[i + 1][(j + (s[i] - '0') * po10[i]) % 13] += dp[i][j];
        dp[i + 1][(j + (s[i] - '0') * po10[i]) % 13] %= P;
      }
    }
  }
  cout << dp[n][5] << endl;
  return 0;
}