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 = list(input())
u = 10**9+7
d = len(S)
dp = np.zeros(13, dtype=np.int64)
dp[0] = 1
m = 1

for i in range(d-1,-1,-1):
    tmp = np.zeros(13, dtype=np.int64)
    a = S[i]
    if a=='?':
        for j in range(10):
            c = j*m
            for k in range(13):
                n = (c+k)%13
                tmp[n] += dp[k]
                tmp[n] %= u
    else:
        c = int(a)*m
        for k in range(13):
            n = (c+k)%13
            tmp[n] += dp[k]
            tmp[n] %= u
    m *= 10
    m %= 13
    dp = tmp
print(dp[5])