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: Runtime Error)

import copy
S = list(input())

nums = [S]
def rec(i):
    global nums
    if i == len(S):
        return 0
    if S[i] == "?":
        tmpnums = copy.deepcopy(nums)
        nums = []
        for n in tmpnums:
            for j in range(10):
                if len(n[i+1:]) > 0:
                    k = n[:i]
                    k.append(str(j))
                    k.extend(n[i+1:])
                else:
                    k = n[:i]
                    k.append(str(j))
                nums.append(k)
        rec(i+1)
    else:
        rec(i+1)
rec(0)
c = 0
for n in nums:
    if int(''.join(n)) % 13 == 5:
        c += 1
print (c % (10 ** 9 + 7))