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 <stdio.h>
#include <stdlib.h>
#include <assert.h>
#include <fstream>
#include <iostream>
#include <sstream>
#include <iomanip>
#include <algorithm>
#include <bitset>
#include <array>
#include <vector>
#include <queue>
#include <set>
#include <cmath> // 変数名にy1が使えなくなるかも…。
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <limits>
#include <functional>
#include <string>

typedef __int128_t int128_t;
std::istream &operator>>(std::istream& input, int128_t& value) { // int128_tの入力。入力が64bitに収まる前提。
    long long tmp; input >> tmp; value = tmp;
    return input;
}
std::ostream &operator<<(std::ostream& output, const int128_t value) { // int128_tの出力。出力が64bitに収まる前提。
    output << (long long)value;
    return output;
}

#define rep(i, begin, end) for(int64_t i = (begin); i <= (end); i++)
#define rev(i, begin, end) for(int64_t i = (begin); (end) <= i; i--)

void printvec(const std::vector<int>& vec) {
    for (int i = 0; i < vec.size(); i++) { std::cout << vec[i] << " "; } std::cout << std::endl;
}

const int MAX_N = 1e5 + 10;
const int MOD = 1e9 + 7;
std::string S;

int128_t dp[MAX_N][20] = {};

int main(int argc, char **argv) {
    std::cin >> S;
    
    dp[0][0] = 1;
    int128_t tmp = 1;
    
    rep (i, 1, S.size()) {
        char c = S[S.size() - i];

        if (c != '?') {
            int128_t num = c - '0';
            int m = (num * tmp) % 13;
            rep (j, 0, 12) {
                int prev = (j - m + 13) % 13;
                dp[i][j] = dp[i-1][prev];
            }
        } else {
            rep (x, 0, 9) {
                int m = (x * tmp) % 13;
                rep (j, 0, 12) {
                    int prev = (j - m + 13) % 13;
                    dp[i][j] += dp[i-1][prev];
                    dp[i][j] %= MOD;
                }
            }
        }
        tmp = (tmp * 10) % 13;
    }

    std::cout << dp[S.size()][5] << std::endl;
    

    return 0;
}