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 sum(int i,int j){
  if(i + j >= 1000000007){return i+j-1000000007;}
  return i+j;
}


int A[100001][13];
int main(){
  int len,res = 1;
  char s[100000];
  scanf("%s",s);
  len = strlen(s);
  A[0][0] = 1;
  for(int i = 0;i < len;i++){
    if(s[len-i-1] == '?'){
      for(int j = 0;j < 10;j++){
        for(int k = 0;k < 13;k++){
        	A[i+1][(j*res+k)%13] = sum(A[i+1][(j*res+k)%13],A[i][k]);
        }
      }
    }
    else{
      int j = s[len-i-1]-'0';
      for(int k = 0;k < 13;k++){
        A[i+1][(j*res+k)%13] = A[i][k];
      }
    }
    res = (res * 10)%13;
  }
  printf("%d\n",A[len][5]);
  return 0;
}