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)

MOD = 10 ** 9 + 7
s = input()
n = len(s)
dp = [[0 for j in range(13)] for i in range(n + 1)]
dp[0][0] = 1
dpi = dp[0]
for i, si in enumerate(s):
    dpi1 = dp[i + 1]
    if si == '?':
        k_list = range(10)
    else:
        k_list = [int(si)]
    for j in range(13):
        xij = dpi[j]
        for k in k_list:
            dpi1[(j * 10 + k) % 13] += xij
    for j in range(13):
        dpi1[j] %= MOD
    dpi = dpi1
print(dp[-1][5])