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)

def f(s):
    rd = [[10, 11, 12], [3, 6, 9], [4, 8, 12], [1, 2, 3], [4, 7, 10], [1, 5, 9]]
    k = len(s)
    md = 10 ** 9 + 7
    dp = [[0] * 13 for _ in range(k + 1)]
    dp[0][0] = 1
    dpi = dp[0]
    for i, c in enumerate(s[::-1]):
        dpi1 = dp[i + 1]
        if c == "?":
            r1, r2, r3 = rd[i % 6]
            sm = sum(dpi)
            for j in range(13):
                dpi1[j] = (sm - (dpi[j - r1] + dpi[j - r2] + dpi[j - r3])) % md
        else:
            m = int(c) * 10 ** i % 13
            for j in range(13):
                dpi1[j] = (dpi1[j] + dpi[j - m]) % md
        dpi = dpi1
    print(dp[k][5])

s = input()
f(s)