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)

import sys

sr = lambda: sys.stdin.readline().rstrip()
ir = lambda: int(sr())
lr = lambda: list(map(int, sr().split()))

def main():
    MOD = 10 ** 9 + 7
    S = sr()
    # 桁DP, 上から
    dp = [[0] * 13 for _ in range(2)]
    dp[0][0] = 1
    for i in range(len(S)):
        num = S[i]
        i %= 2
        if num.isdigit():
            num = int(num)
            for j in range(13):
                dp[1-i][(10*j+num)%13] = dp[i][j]
        else:
            dp[1-i] = [0] * 13
            for j in range(13):
                for k in range(10):
                    dp[1-i][(10*j+k)%13] += dp[i][j]
                dp[1-i][j] %= MOD

    answer = dp[len(S)%2][5]
    print(answer%MOD)

if __name__ == '__main__':
    main()