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: Accepted)

#!/usr/bin/env python3
import sys

MOD = 1000000007  # type: int

def solve(S: str):
    N = len(S)
    r_d = [1] * (N+1)
    r_d[0] = 0
    for i in range(2, N+1):
        r_d[i] = (r_d[i-1] * 10) % 13
    
    dp = [[0 for j in range(N+1)] for i in range(13)] # dp[i][j]: 13でわってiになるSのj桁目まで数の総数
    dp[0][0] = 1

    for j in range(1, N+1):
        d = S[-j]
        if d != "?":
            d = (int(d) * r_d[j]) % 13
            for i in range(13):
                dp[i][j] += dp[(i - d) % 13][j-1]
            continue
        for k in range(10):
            d = (k * r_d[j]) % 13
            for i in range(13):
                dp[i][j] += dp[(i - d) % 13][j-1]
                dp[i][j] %= MOD
    print(dp[5][N])
    return


# Generated by 1.1.4 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
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
    solve(S)

if __name__ == '__main__':
    main()