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 <iostream>
#include <string>
#include <vector>
using namespace std;
typedef long long ll;

ll mod = 1000000007;
string S;
vector<vector<ll>> dp(100005,vector<ll>(13,0));

int main(){
    cin >> S;
    int N = (int)S.size();

    for (int i = 0; i < N;i++){
        char c = (char)S[i];
        int t = c - '0';
        if(c == '?')
            t = -1;
        dp[0][0] = 1;
        for (int j = 0; j < 10;j++){
            if(t != -1 && t != j)
                continue;
            for (int k = 0; k < 13;k++){
                dp[i + 1][(k * 10 + j) % 13] += dp[i][k];
            }
        }
        for (int j = 0; j < 13;j++){
            dp[i + 1][j] %= mod;
        }
    }
    cout << dp[N][5] << endl;
    return 0;
}