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 MAX_S 100000
#define MOD 1000000007

int dp[MAX_S+1][13]={};
int i,j,k,s;

int main(void){
    char S[MAX_S];
    scanf("%s",S);
    int m[6] = {1,10,9,12,3,4};
    
    for(i=0;i<13;i++){
        if(S[strlen(S)-1]=='?'){
            if(i<10)dp[0][i]=1;
            else dp[0][i]=0;
        }else{
            s = S[strlen(S)-1] -48;
            if(s==i)dp[0][i]=1;
            else dp[0][i]=0;
        }
    }

    for(i=1;i<strlen(S);i++){
        if(S[strlen(S)-1-i]=='?'){
            for(j=0;j<13;j++){
                for(k=0;k<10;k++){
                    dp[i][(k*m[i%6]+j)%13]= (dp[i][(k*m[i%6]+j)%13]+dp[i-1][j])%MOD;
                }
            }
            
        }else{
            s = S[strlen(S)-1-i] -48;
            for(j=0;j<13;j++){
                    dp[i][(s*m[i%6]+j)%13]= (dp[i][(s*m[i%6]+j)%13]+dp[i-1][j])%MOD;
            }
        }
    }
    printf("%d",dp[strlen(S)-1][5]);
    return 0;
}