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)

# standart input
# n = int(input())
# a = list(map(int, input().split()))

N = 13
MOD = 10 ** 9 + 7

s = input()[::-1]

dp = [0 for i in range(N)]
nextdp = [0 for i in range(N)]
zeros = [0 for i in range(N)]
dp[0] = 1

r = 1
for i, si in enumerate(s):
    nextdp = zeros[:]

    for j in range(10):
        jj = j
        if si == "?":
            pass
            # c = (j * 10 ** i) % N
        elif j == 0:
            jj = int(si)
        else:
            break

        for k in range(N):
            l = (k + r * jj) % N
            nextdp[l] = (nextdp[l] + dp[k]) % MOD

    dp = nextdp
    r = r * 10 % N

print(dp[5])