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 <malloc.h>
#include <math.h>
#include <stdio.h>
#include <string.h>
#include <stdlib.h>

int main(void) {
  int n, k, i, cou=0, tmp, len, m;
  long long mod=1000000007;
  char s[100000];
  scanf("%s", s);
  for(len=0; s[len] != '\0'; ++len)
    ; //文字数
  long long dp[len + 1][13]; //dp[上n桁まで][13で割った余り]

  for(i=0; i < len + 1; i++)
    for(k=0; k < 13; k++)
      dp[i][k]=0;

  if(s[0] == '?') for(k=0; k < 10; k++)
    dp[1][k]=1;
  else dp[1][s[0] - 48]=1;

  for(i=1; i < len; i++){
    for(k=0; k < 13; k++){
      if(s[i] == '?'){
        for(m=0; m < 10; m++){
          tmp=(10 * k + m) % 13;
          dp[i + 1][tmp]=(dp[i + 1][tmp] + dp[i][k]) % mod;
        }
      }else{
        tmp=(10 * k + s[i] - 48) % 13;
        dp[i + 1][tmp]=(dp[i + 1][tmp] + dp[i][k]) % mod;
      }
    }
  }
  printf("%lld", dp[len][5]);
  return 0;
}