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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

rotate = lambda x,y: x[-y:] + x[:-y]
S = input()
S = "??2??5"
mod = 13
amari = 5
dp_tmp = [0]*13
dp_tmp[0] = 1
mul = 1
for s in S[::-1]:
    dp = [0]*13
    if s == "?":
        for n in range(10):
            dp_tmp_roll = rotate(dp_tmp,n*mul%mod)
            for k in range(13):
                dp[k] += dp_tmp_roll[k]
    else:
        dp_tmp_roll = rotate(dp_tmp,int(s)*mul%mod)
        for k in range(13):
            dp[k] += dp_tmp_roll[k]
    for n in range(13):
        dp[n] = dp[n]%(10**9+7)
    dp_tmp = dp
    mul = mul*10%13
print(dp[amari])