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)

MOD = 10 ** 9 + 7
qTable = [[(j * i) % 13 for j in range(13)] for i in range(11)]

S = input()

C, tC, qi = [1] + [0] * 12, [0] * 13,  1

for i in range(len(S)):
    if S[-(i + 1)] == '?':
        tC = [0] * 13
        for j in range(10):
            q = qTable[j][qi]
            for c in range(13):
                tC[(c + q) % 13] += C[c]
    else:
        q = qTable[int(S[-(i + 1)])][qi]
        for c in range(13):
            tC[(c + q) % 13] = C[c]

    qi = qTable[10][qi]
    for c in range(13):
        C[c] = tC[c] % MOD

print(C[5] % MOD)