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)

#!/usr/bin/env python3
import sys

MOD = 1000000007  # type: int


def solve(S: str):
    """
    >>> solve("05")
    1
    >>> solve("18")
    1
    >>> solve("13")
    0
    """
    pre, cur = [0] * 13, None
    base = 10
    if S[-1] == "?":
        cur = [1] * 10 + [0] * 3
    else:
        cur = [0] * 13
        cur[int(S[-1])] = 1
    for n in reversed(S[:-1]):
        pre, cur = cur, pre
        for i in range(13): # 再生成を避ける
            cur[i] = 0
        g = range(10) if n == "?" else [int(n)]
        for i in g:
            t = base * i % 13
            for j in range(13):
                cur[(j+t)%13] = (cur[(j+t)%13] + pre[j]) % MOD
        base = (base * 10) % 13        
        # print(n, pre, cur, base)
    return cur[5]

# Generated by 1.1.7.1 https://github.com/kyuridenamida/atcoder-tools
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    S = next(tokens)  # type: str
    print(solve(S))

def test():
    import doctest
    doctest.testmod()

if __name__ == '__main__':
    test()
    main()