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: Accepted)

words = lambda t : list(map(t, input().split()))
s = input()
rs = reversed(s)

a = []
cur_mod_10_pow = 1
v = 0
for i,c in enumerate(rs):
    if c == "?":
        a.append(cur_mod_10_pow)
    else:
        v += (int(c) * cur_mod_10_pow) % 13
        v %= 13
    cur_mod_10_pow *= 10
    cur_mod_10_pow %= 13

#print(v, list(reversed(a)))
MOD = 1000000007
prev = [0] * 13
prev[0] = 1
#print(prev)
for aa in a:
    cur = [0 for _ in range(13)]
    for i,p in enumerate(prev):
        #print(i,p, cur)
        for j in range(10):
            #print(i,j,(i+aa*j) % 13)
            cur[(i+(aa*j)) % 13] += p
            cur[(i+aa*j) % 13] %= MOD
    #print(cur)
    prev = cur

print(prev[(5-v)%13])