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 DIV 1000000007

int main(){
  char S[100002],tmp[100002];
  int N;
  int cnt[2][13];
  int mod;
  
  scanf( "%s", tmp);
  N = strlen(tmp);
  for(int i=0;i<N;i++)
    S[i] = tmp[N-1-i];
  
  for(int i=0;i<13;i++)
    cnt[1][i] = 0;
  mod = 1;
  cnt[1][0] = 1;
  
  for( int i=0; i<N; i++){
    if ( S[i] == '?' ){
      for( int j=0; j<13; j++)
	cnt[i%2][j] = 0;
      for( int n=0; n<10; n++)
	for( int j=0; j<13; j++)
	  cnt[i%2][(j+n*mod)%13] = (cnt[i%2][(j+n*mod)%13]+cnt[(i+1)%2][j]) % DIV;
    }else
      for( int j=0; j<13; j++)
	cnt[i%2][(j+(S[i]-'0')*mod)%13] = cnt[(i+1)%2][j];

    mod = (mod*10)%13;
  }  
    
  printf("%d\n",cnt[(N-1)%2][5]);
  
  return 0;
}