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 PyPy3 (2.4.0) (judge verdict: Accepted)

import sys

sys.setrecursionlimit(10 ** 7)
f_inf = float('inf')
mod = 10 ** 9 + 7


def resolve():
    s = input()
    L = len(s)
    dp = [[0] * 13 for _ in range(L + 1)]
    dp[0][0] = 1

    for i in range(L):
        for j in range(13):
            if s[i] == "?":
                for k in range(10):
                    dp[i + 1][(j * 10 + k) % 13] += dp[i][j] % mod
            else:
                k = int(s[i])
                dp[i + 1][(j * 10 + k) % 13] += dp[i][j] % mod

    print(dp[-1][5] % mod)


if __name__ == '__main__':
    resolve()