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: Wrong Answer)

mod = 10 ** 9 + 7

s = input()

cur = [0] * 13
c = s[-1]
if c != '?':
    cur[int(c)] = 1
else:
    for j in range(10):
        cur[j] = 1

d = 10
for c in s[::-1]:
    if c != '?':
        l = [int(c)]
    else:
        l = [j for j in range(10)]
    tmp = [0] * 13
    for j in l:
        for k in range(13):
            ind = (j * d + k) % 13
            tmp[ind] += cur[k] % mod
    cur = tmp
    d *= 10
print(cur[5])