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 = input()
 
MOD = 10**9+7
 
dp = [[0]*13 for _ in range(len(S) + 1)]
 
 
dp[0][0] = 1
 
for index in range(1, len(S) + 1):
    s = S[len(S) - index ]
    mul = (10 ** (index - 1)) % 13
    if s == '?':
        for pre_index in range(13):
            for i in range(10):
                next_i = (i * mul  +  pre_index ) % 13
                dp[index][next_i] += dp[index - 1][pre_index] 
    else:
        for pre_index in range(13):
            i = int(s)
            next_i = (i * mul +  pre_index ) % 13
            dp[index][next_i] += dp[index - 1][pre_index] 
 
    for i in range(13):
        dp[index][i] %= MOD
 
 
 
print(dp[len(S)][5])