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 (7.3.0) (judge verdict: Time Limit Exceeded)

s = list(input())[::-1]
n = len(s)
mod = 10**9 + 7

t = [[0 for j in range(13)] for i in range(n)]
for i,x in enumerate(s):
    if i == 0:
        if x == "?":
            for j in range(0,10):
                t[i][j] += 1
        else:
            t[i][int(x)] += 1
    else:
        if x == "?":
            for k in range(13):
                for j in range(10):
                    b = (k + j*pow(10, i ,13))%13
                    t[i][b] += t[i-1][k]
                    t[i][b] %= mod
        else:
            for k in range(0,13):
                b = (k + int(x)*pow(10, i ,13))%13
                t[i][b] += t[i-1][k]
                t[i][b] %= mod
print(t[-1][5]%mod)