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: Wrong Answer)

S = input()
N = 13
dp = [0] * N
dp[0] = 1
mul = 1
mod = 10 ** 9
for i in range(len(S)-1, -1, -1):
    i = int(i)
    nextDp = [0] * N
    char = S[i]
    if char == '?':
        for k in range(10):
            for j in range(N):
                nextDp[(k * mul + j)%13] += dp[j]
                nextDp[(k * mul + j)%13] %= mod
    else:
        k = int(S[i])
        for j in range(N):
            nextDp[(k * mul + j)%13] += dp[j]
            nextDp[(k * mul + j)%13] %= mod
    mul *= 10
    mul %= N
    dp = nextDp
print(dp[5])