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)

S = input()
#S = "?" * 100000
S = S[::-1]
N = 13
mod = 10 ** 9 + 7
dp = [0] * 26
dp[13] = 1
digit = 1
for c in range(len(S)):
    dp[:13] = [0] * N
    if S[c] == '?':
        for k in range(10):
            for j in range(N):
                dp[(k * digit + j) % N] += dp[j + 13]
                dp[(k * digit + j) % N] %= mod
    else:
        k = int(S[c])
        for j in range(N):
            #index = (k * digit + j) % N
            dp[(k * digit + j) % N] += dp[j + 13]
            dp[(k * digit + j) % N] %= mod

    digit *= 10
    digit %= N
    #print(dp)
    dp[13:26] = dp[:13]
    #print(dp)
print(dp[5])