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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define maxn 100005
using namespace std;
typedef long long ll;
char str[maxn];
ll dp[maxn][20];
const int mod=1e9+7;
int main()
{
    scanf("%s",str+1);
    int len=strlen(str+1);
    dp[0][0]=1;
    for(int i=1;i<=len;i++){
        if(str[i]!='?'){
            for(int j=0;j<13;j++){
                dp[i][(j*10+str[i]-'0')%13]=(dp[i][(j*10+str[i]-'0')%13]+dp[i-1][j])%mod;
            }
        }
        else{
            for(int j=0;j<=9;j++){
                for(int k=0;k<13;k++){
                    dp[i][(k*10+j)%13]=(dp[i][(k*10+j)%13]+dp[i-1][k])%mod;
                }
            }
        }
    }
    printf("%lld\n",dp[len][5]);
    return 0;
}