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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

def main():
    MOD = 10**9 + 7
    S = input()
    N = len(S)
    dp = [[0 for _ in range(13)] for _ in range(N + 1)]
    dp[0][0] = 1
    for i, c in enumerate(S):
        for j in range(10):
            if c != '?' and c != str(j):
                continue
            for k in range(13):
                dp[i + 1][(10 * k + j) % 13] += dp[i][k]
                dp[i + 1][(10 * k + j) % 13] %= MOD
    print(dp[N][5])


if __name__ == '__main__':
    main()