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)

def main():
    MOD = 7 + 10**9
    S = tuple(input())
    N = len(S)
    dp = [[0]*13 for _ in range(N+1)]
    dp[0][0] += 1
    for i in range(N):
        for k in range(13):
            if S[-(i+1)] != '?':
                dp[i+1][(k+int(S[-(i+1)])*(10**(i))%13)%13] += dp[i][k] 
                dp[i+1][(k+int(S[-(i+1)])*(10**(i))%13)%13] %= MOD
            else:
                for l in range(10):
                    dp[i+1][(k+l*(10**(i))%13)%13] += dp[i][k]
                    dp[i+1][(k+l*(10**(i))%13)%13] %= MOD
    print(dp[-1][5])

if __name__ == '__main__':
    main()