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: Time Limit Exceeded)

s = input()
len_s = len(s)
mod = 10 ** 9 + 7
dp = [[0] * 13 for i in range(len_s)]

for i in range(len_s):
    if s[-(i + 1)] == '?':
        for j in range(13):
            if i == 0:
                if j < 10:
                    dp[i][j] = 1
                continue

            if dp[i - 1][j] > 0:
                for k in range(10):
                #k:先頭に加える数字
                    add = k * pow(10, i)
                    dp[i][(j + add)%13] = (dp[i][(j + add)%13] + dp[i - 1][j])%mod

    else:
        if i == 0:
            dp[i][int(s[-(i + 1)])] = 1
            continue

        add = int(s[-(i + 1)]) * pow(10, i)
        for j in range(13):
            if dp[i - 1][j] > 0:
                dp[i][(j + add)%13] = (dp[i][(j + add)%13] + dp[i - 1][j])%mod

print(dp[-1][5] % mod)