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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

from functools import reduce

S = input()

# 末尾から各あまりについてDP
M = 13
MOD = 10**9 + 7
ans = reduce(
    lambda acc, c: (
        [
            sum(
                acc[0][(i - acc[1] * j) % M]
                for j in range(10)
            ) % MOD
            for i in range(M)
        ] if c == '?' else
        [
            acc[0][(i - acc[1] * int(c)) % M]
            for i in range(M)
        ],
        (10 * acc[1]) % M
    ),
    S[::-1],
    (
        [
            1 if i == 0 else
            0
            for i in range(M)
        ],
        1
    )
)[0][5]

print(ans)