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: Time Limit Exceeded)

from sys import stdin


def fetch_one_line():
    return stdin.readline().rstrip()


def fetch_int_input():
    return [int(s) for s in fetch_one_line().split()]


def fetch_inputs(times):
    return [fetch_one_line() for _ in range(times)]


def fetch_int_inputs(times):
    return [[int(s) for s in fetch_one_line()] for _ in range(times)]


def fetch_ints_inputs(times):
    return [fetch_int_input() for _ in range(times)]


ipt = fetch_one_line()
DIVIDE_NUM = 13
remainds = [[0 for _ in range(DIVIDE_NUM)]]
remainds[0][0] = 1

def transrate(matrix):
    return list(map(list, zip(*matrix)))

def make_remind(latest_remind, digit):
    tmp_remind = [[latest_remind[(j - (i * (digit % 13))) % 13] for j in range(DIVIDE_NUM)]
            for i in range(10)]

    return [sum(t) for t in transrate(tmp_remind)]

for idx, s in enumerate(ipt[::-1]):
    if s == "?":
        digit = pow(10, idx)
        remainds.append(make_remind(remainds[-1], digit))
    else:
        int_s = int(s)
        digit = pow(10, idx)
        move = (int_s % 13) * (digit % 13)
        new_remaind = [remainds[-1][(i - move) % 13] for i in range(DIVIDE_NUM)]
        remainds.append(new_remaind)

print(remainds[-1][5] % (pow(10, 9) + 7))