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: Time Limit Exceeded)

import numpy as np

s = input()[::-1]

dp = np.zeros((len(s),13), dtype="uint64")

if s[0] =="?":
    dp[0] = [1]*10+[0]*3
else:
    dp[0][int(s[0])] =1

L1 = range(1, len(s))

for i in L1:
    if s[i] == "?":
        mod = pow(10, i, 13)
        mod_list = ((mod*i)%13 for i in range(10))
        for j in mod_list:
            dp[i, :] += np.roll(dp[i - 1, :], j)
        dp[i, :] %= (10**9+7)
    else:
        mod = (pow(10, i, 13)*int(s[i]))%13
        dp[i, :] += np.roll(dp[i - 1, :], mod)

print(int(dp[-1][5])%(10**9+7))