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>
#include<math.h>
#include<stdlib.h>
#include<limits.h>

#define rep(i,begin,end) for(int i=begin; i<end; i++)
#define revrep(i,begin,end) for(int i=begin; i>end; i--)
#define lld long long int

#define MOD 1000000007

int main(){
    char s[100001];
    scanf("%s", s);
    int len = strlen(s);
    int dp[len+1][13];
    rep(i, 0, len+1){
        rep(j, 0, 13){
            dp[i][j] = 0;
        }
    }
    dp[0][0] = 1;
    rep(i, 1, len+1){
        if(s[i-1] == '?'){
            rep(j, 0, 13){
                rep(k, 0, 10){
                    dp[i][(j*10 + k) % 13] += dp[i-1][j];
                    dp[i][(j*10 + k) % 13] %= MOD;
                }
            }
        }else{
            rep(j, 0, 13){
                dp[i][(j*10 + (s[i-1]-'0')) % 13] += dp[i-1][j];
                dp[i][(j*10 + (s[i-1]-'0')) % 13] %= MOD;
            }
        }
        rep(j, 0, 13){
            dp[i][j] %= MOD;
        }
    }
    printf("%d", dp[len][5]);

    return 0;
}