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: Runtime Error)

import numpy as np
MOD = 1000000007
s = [int(x) if x!="?" else -1 for x in input()]
dp = np.full((len(s), 13), 0, dtype="int64")
 
if s[0] == -1:
    dp[0][0:10] = 1
else:
    dp[0][int(s[0])] = 1
 
table = [ s % 13 for s in range(130)]
for index in range(1, len(s)):
    if not s[index] == -1:
        value = int(s[index])
 
        for old_amari in range(13):
            new_amari = (table[old_amari * 10] + value) % 13
            dp[index][new_amari] += dp[index-1][old_amari]
    else:
        for value in range(10):
            for old_amari in range(13):
                new_amari = (table[old_amari * 10] + value) % 13
                dp[index][new_amari] += dp[index - 1][old_amari]
 
    dp[index] = dp[index] % MOD
 
print(dp[len(s)-1][5])