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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

from collections import defaultdict


def main():
    S = {i:s for i, s in enumerate(input()[::-1])}
    MOD = 10**9 + 7

    DP_table = defaultdict(int)
    
    digit = S[0]
    if digit == '?':
        for i in range(10):
            DP_table[(1, i)] = 1
    else:
        DP_table[(1, int(digit))] = 1
    
    power_ten = 1
    for i in range(1, len(S)):
        digit = S[i]
        power_ten *= 10
        if digit == '?':
            for j in range(10):
                devided = j * power_ten
                for k in range(13):
                    surplus = (devided + k) % 13
                    DP_table[(i + 1, surplus)] += DP_table[(i, k)] % MOD
                    DP_table[(i + 1, surplus)] %= MOD
        else:
            for k in range(13):
                surplus = (int(digit) * power_ten + k) % 13
                DP_table[(i + 1, surplus)] += DP_table[(i, k)] % MOD
                DP_table[(i + 1, surplus)] %= MOD
                
    print(DP_table[(len(S), 5)])

if __name__ == "__main__":
    main()