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()
dp1 = [0] * 13
dp2 = [0] * 13
dp1[0] = 1
n = len(s)

for i in range(n):
    if s[n-i-1] != "?":
        a = (int(s[n-i-1]) * 10 ** i) % 13
        for j in range(13):
            dp2[j] = dp1[j-a]
    else:
        for k in range(10):
            a = (k * 10 ** i) % 13
            for j in range(13):
                dp2[j] += dp1[j-a]
    dp1 = dp2
    dp2 = [0] * 13

print(dp1[5]%(10**9 + 7))