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)

S = input()
MOD = 10**9 + 7

dp = [[0] * 13 for _ in range(2)]
dp[0][0] = 1

n = len(S)
for i in range(n):
    if i == 0:
        mod_array = [i for i in range(10)]
    else:
        mod_array = [i * 10 % 13 for i in mod_array]
    s = S[n-i-1]
    if s == '?':
        for a in mod_array:
            for k in range(13):
                dp[1][(k+a)%13] += dp[0][k]
    else:
        a = mod_array[int(s)]
        for k in range(13):
            dp[1][(k + a) % 13] += dp[0][k]
    for k in range(13):
        dp[0][k] = dp[1][k] % MOD
        dp[1][k] = 0

print(dp[0][5])