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 Python (3.4.3) (judge verdict: Accepted)

import numpy as np


def solve(s):
    MOD = 10 ** 9 + 7
    dp = np.zeros(13, dtype=np.int64)
    dp[0] = 1
    idx = np.zeros(13, dtype=np.int8)
    for i in range(13):
        idx[i * 10 % 13] = i
    window = np.ones(10, dtype=np.int8)
    for c in s:
        if c == '?':
            tdp = dp[idx]
            ndp = np.concatenate([tdp[4:], tdp])
            dp = np.convolve(ndp, window, mode='valid') % MOD
        else:
            dp = np.roll(dp[idx], int(c))
    return dp[5]


s = input()
print(solve(s))