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>

#define MOD 1000000007
#define N 100005

int main(void)
{
  int n;
  char s[N];
  long long dp[N][13]; //先頭i文字を13で割ったあまりがjであるもののパターン数

  int i, j, k;
  scanf("%s", s);
  n = strlen(s);

  dp[0][0] = 1;

  for (i = 1; i <= n; i++)
  {
    if (s[i - 1] == '?')
    {
      for (j = 0; j < 10; j++)
        for (k = 0; k < 13; k++)
          dp[i][(k * 10 + j) % 13] += dp[i - 1][k];
    }
    else
    {
      for (k = 0; k < 13; k++)
        dp[i][(k * 10 + (s[i - 1] - '0')) % 13] += dp[i - 1][k];
    }

    for (j = 0; j < 13; j++)
      dp[i][j] %= MOD;
  }

  printf("%lld\n", dp[n][5]);
  return 0;
}