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: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;

int mod = 1'000'000'007;

long long modpow(long long a, long long b, int p){
    if (b == 0) return 1;
    if (b % 2) return a * modpow(a, b - 1, p) % p;
    return modpow(a, b / 2, p) * modpow(a, b / 2, p) % p;
}

int main(){
    string s;
    cin >> s;
    int k = s.size();
    vector<long long> dp(13, 0);
    dp[0] = 1;
    for (int i = 0; i < k; i++){
        vector<long long> next_dp(13, 0);
        long long tmp = modpow(10, k - i - 1, 13);
        if (s[i] == '?'){
            for (int j = 0; j < 13; j++) {
                for (int z = 0; z < 10; z++){
                    next_dp[(tmp * z % 13 + j) % 13] += dp[j];
                }
            }
        }
        else {
            for (int j = 0; j < 13; j++){
                next_dp[(tmp * (s[i] - '0') % 13 + j) % 13] += dp[j];
            }
        }
        dp = next_dp;
    }
    cout << dp[5] % mod << endl;
}