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)

S = input()[::-1]

a = [0] * 13
n = [0] * 13

def calc(d, num):
#    shift = (num * (10 ** d))%13
    shift = num
    for _ in range(d):
        shift *= 10
        shift %= 13
    if d==0:
        n[shift] = 1
    else:
        for i in range(13):
            n[(i+shift)%13] += a[i]
    

for d, s in enumerate(S):
    if s=='?':
        for i in range(10):
            calc(d, i)
    else:
        calc(d, int(s[0]))
    a, n = n, a
    for i in range(13):
        a[i] %= 1000000007
        n[i] = 0

print(a[5])