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)

S = str(input())
S_len = len(S)

DP = list = [[0] * 13 for i in range(S_len)]

for i in reversed(range(S_len)):

    if i == len(S) - 1:
        if S[i] != "?":
            DP[i][int(S[i]) % 13] = 1
        else:
            for j in range(10):
                DP[i][j] = 1

    else:

        if S[i] != "?":
            for j in range(13):
                if DP[i + 1][j] != 0:
                    DP[i][(j + int(S[i]) * (10 ** (S_len - 1 - i))) % 13] = (DP[i][(j + int(S[i]) * (
                                10 ** (S_len - 1 - i))) % 13] + DP[i + 1][j]) % 1000000007
        else:
            for j in range(13):
                for k in range(10):
                    if DP[i + 1][j] != 0:
                        DP[i][(j + k * (10 ** (S_len - 1 - i))) % 13] = (DP[i][
                                                                              (j + k * (10 ** (S_len - 1 - i))) % 13] +
                                                                          DP[i + 1][j]) % 1000000007

print(DP[0][5])