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 (7.3.0) (judge verdict: Runtime Error)

from functools import lru_cache

S = input().strip()

MOD = 10 ** 9 + 7

lens = len(S)

sys.setrecursionlimit(10 ** 8)

@lru_cache(maxsize=None)
def solve(amari, keta):
    if keta == lens - 1:
        if S[keta] == "?":
            cnt = 0
            for i in range(9, -1, -1):
                if (amari + i) % 13 == 5:
                    cnt += 1
            return cnt
        else:
            if (amari + int(S[keta])) % 13 == 5:
                return 1 % MOD
            else:
                return 0
    else:
        if S[keta] == "?":
            x = 0
            for i in range(9, -1, -1):
                x += solve((amari + (i * 10 ** (lens - 1 - keta)) % 13) % 13, keta + 1)
            return x % MOD
        else:
            return solve((amari + (int(S[keta]) * 10 ** (lens - 1 - keta)) % 13) % 13, keta + 1) % MOD


print(solve(0, 0) % MOD)