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 (Clang 3.8.0) (judge verdict: Accepted)

#include <iostream>
#include <map>
#include <vector>
#include <algorithm>
#include <string>
#include <queue>

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

typedef long long int lli;
using namespace std;
typedef pair<int, int> ii;
typedef priority_queue<int, vector<int>, greater<int> > heapq;
#define int long long int

const lli MOD = 1000000007LL;
inline lli mod_mul(lli x, lli y) {
    return (x * y) % MOD;
}
inline lli mod_add(lli x, lli y) {
    return (x + y) % MOD;
}

signed main() {
    string S; cin >> S;
    int len = S.length();
    reverse(S.begin(), S.end());

    // int dp[100001][13];
    vector< vector<int>> dp(len + 1, vector<int>(13, 0));
    dp[0][0] = 1;

    int digit = 1;
    for (int i = 1; i <= len; i++) {
        char c = S[i - 1];
        if (c != '?') {
            int p = c - '0';
            int r = (p * digit) % 13;
            for (int j = 0; j < 13; j++) {
                dp[i][j] = dp[i - 1][(13 + j - r) % 13];
            }
        } else {
            for (int p = 0; p < 10; p++) {
                int r = (p * digit) % 13;
                for (int j = 0; j < 13; j++) {
                    dp[i][j] = mod_add(dp[i][j], dp[i - 1][(13 + j - r) % 13]);
                }
            }
        }
        digit = (digit * 10) % 13;
    }
    cout << dp[len][5] << endl;
    return 0;
}