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;
#define M 1000000007;

long long dp[100001][13];

void rep(int x, int u, long long mul){
  if ( u == 1){
    dp[1][x] = 1;
    return;
  }
  for (int j = 0; j < 13; j++ ){
    dp[u][(x*mul+j)%13] += dp[u-1][j];
    dp[u][(x*mul+j)%13] %= M;
  }
}

int main(){
  string s;
  cin >> s;
  int c, n = s.length();

  for ( int i = 0; i<=100001; i++){
    for ( int j = 0; j < 13; j++){
      dp[i][j] = 0;
    }
  }

  long long mul = 1;
  for ( int i = n-1; i >= 0; i--){
    if ( s[i] == '?') c = -1;
    else c = s[i] - '0';

    for ( int j = 0; j <= 9; j++){
      if ( c != -1 && c != j )continue;
      rep(j, n-i, mul);
    }
    mul *= 10;
    mul %= 13;
  }

  cout << dp[s.length()][5] << endl;

  return 0;
}