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 = str(input())
MOD = 1000000007
tmp = 0
for i in range(len(s)):
    if s[i] == "?":
        tmp += 1
    else:
        break

keta = len(s) - tmp
n = 10 ** len(s) // 13 + 1
ans = 0
flg = False
for i in range(n):
    step = str(i * 13 + 5)
    if keta <= len(str(step)) <= len(s):
        print(step)
        for j in range(1, keta+1):
            if s[-j] == "?":
                pass
            elif step[-j] != s[-j]:
                flg = False
                break
            elif step[-j] == s[-j]:
                flg = True
        print(flg)
    if flg:
        ans += 1 % MOD

print(ans)