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>
using namespace std;

static const unsigned long long MOD = 1000000007LL;

int main() {
    
    char s[100005];
    uint64_t dp[100005][13];

    cin >> s;

    dp[0][0] = 1;
    int n = strlen(s);
    for(int i = 0; i < n; i++) {
        int num;
        if (s[i] != '?') num = s[i] - '0';
        else num = -1;

        for(int j = 0; j < 10; j++) {
            if (num != -1 && num != j) continue;
            for (int k = 0; k < 13; k++) {
                dp[i + 1][(k * 10 + j) % 13] += dp[i][k];
            }
        }

        for(int j = 0; j < 13; j++) {
            dp[i+1][j] %= MOD;
        }
    }
    uint64_t ans = dp[n][5] % MOD;
    cout << ans;

    return 0;
}