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)

#goalまでNます
S = list(input())

cnt = S.count("?")
list = []

for i in range(len(S)):

    if S[i]=="?":
        list.append(i)
    else:
       S[i] = int(S[i])
count = []

print(list)


def search(n, k, S):

    #最後まできた時
    if n==cnt:
        S[list[n-1]] = k
        print(S)
        test = 0
        for i in range(len(S)):
            test = test + S[i]*10**(len(S)-i-1)
        if (int(test) % 13) == 5:
            count.append(1)
        return

    S[list[n-1]] = k

    for i in range(0, 10, 1):
        search(n+1, i, S)

for i in range(0, 10, 1):
    search(1, i, S)

print(len(count))