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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <string.h>

int main(void)
{
  long MOD = 1000000007;
  char s[100005];
  scanf("%s", s);
  long dp[100005][13];
  int n = strlen(s);
  dp[0][0] = 1;

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

    for(int j = 0; j < 10; j++){
      if(c != -1 && c != j)
        continue;
      for(int ki = 0; ki < 13; ki++)
        dp[i+1][(ki*10+j)%13] += dp[i][ki];
    }
    for(int j = 0; j < 13; j++)
      dp[i+1][j] %= MOD;
  }
  printf("%ld\n", dp[n][5]);
  return 0;
}