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)

#define _USE_MAT_DEFINES
#include<iostream>
#include <iomanip>
#include<stdio.h>
#include<string>
#include<vector>
#include<algorithm>
#include<cmath>
#include <queue>
#include <utility>
#include <map>
#include <set>
#include <stack>
#include <deque>
#include <numeric>
#include <functional>
using namespace std;

#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
#define INF 1e9
#define MOD 1000000007;//1e9+7

int main() {
    string S;
    cin >> S;
    int N = S.size();
    //dp[i][j]=上からi桁決めたときに13で割ってj余る数の総数をMODで割ったあまり
    vector<vector<long long>>dp(N + 1, vector<long long>(13, 0));
    dp[0][0] = 1;

    rep(i, N) {
        int d = (S[i] == '?') ? (-1) : (S[i] - '0');
        rep(k, 10) {
            if (d != -1 && d != k)continue;
            rep(j, 13) {
                int ni = i + 1, nj = (j * 10 + k) % 13;
                dp[ni][nj] += dp[i][j];
                dp[ni][nj] %= MOD;
            }
        }
    }
    cout << dp[N][5];

    return 0;
}