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 rep(i,n,m) for(int i = (n); i <(m); i++)
using namespace std;
using ll = long long;
ll dp[1000000][13];
const ll MOD = 1000000007;

int main()
{
    string s;
    cin >> s;

    dp[0][0] = 1;
    rep(i, 0, s.size())
    {
        if (s[i] == '?')
        {
            rep(k, 0, 10)
            rep(j, 0, 13)
            {
                dp[i + 1][(j * 10 + k) % 13] += dp[i][j];
                dp[i + 1][(j * 10 + k) % 13] %= MOD ;
            }
        }
        else
            rep(j, 0, 13)
            {
                int k = s[i] - '0';
                dp[i + 1][(j * 10 + k) % 13] += dp[i][j];
                dp[i + 1][(j * 10 + k) % 13] %= MOD;
            }
        // rep(j, 0, 13)
        //     cout << i << ' ' << j << ' ' << dp[i + 1][j] << endl;
    }
    cout << dp[s.size()][5] << endl;
    return 0;
}