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: Accepted)

MOD = 10**9 + 7

def main():
    s = [int(in_i) if in_i != '?' else -1 for in_i in list(open(0).read())[:-1]]
    n = len(s)

    cnt = [0] * 13
    if s[0] == -1:
        for j in range(10):
           cnt[j] = 1
    else:
        cnt[s[0]] = 1

    for cur_s in s[1:]:
        dp = [0] * 26
        for i in range(13):
            dp[i*10%13] = cnt[i] % MOD
        dp[13:] = dp[:13]

        if cur_s == -1:
            for i in range(13):
                cnt[i] = sum(dp[i+4:i+14])
        else:
            for i in range(13):
                cnt[i] = dp[i+13-cur_s]

    ans = cnt[5] % MOD
    print(ans)
    return()

if __name__ == '__main__':
    main()