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)

mod = 10**9+7
S = input()
N = len(S)
dp = [[0]*13 for _ in range(N+1)]
dp[0][0] = 1
S = S[::-1]
for i in range(N):
    if S[i] != '?':
        m = int(S[i])
        rm = (m*pow(10,i,13))%13
        for r in range(13):
            dp[i+1][(r+rm)%13] = dp[i][r]
            dp[i+1][(r+rm)%13] %= mod
    else:
        for m in range(10):
            rm = (m*pow(10,i,13))%13
            for r in range(13):
                dp[i+1][(r+rm)%13] += dp[i][r]
                dp[i+1][(r+rm)%13] %= mod

print(dp[N][5])