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)

import sys
input = sys.stdin.readline
 
MOD = 10**9 + 7
def main():
    S = input()
    N = len(S)-1
 
    if S[0] == '?':
        dp = [1,1,1,1,1,1,1,1,1,1,0,0,0]
    else:
        dp = [0,0,0,0,0,0,0,0,0,0,0,0,0]
        dp[int(S[0])] = 1
 
    for i in range(1,N):
        dppre = dp
        dp = [0] * 13
 
        if S[i] == '?':
            for j in range(13):
                for k in range(10):
                    dp[(j * 10 + k) % 13 ] += dppre[j]
        else:
            for j in range(13):
                dp[(j * 10 + int(S[i])) % 13 ] += dppre[j]
 
        for j in range(13):
            dp[j] %= MOD
 
    print(dp[5])
if __name__ == '__main__':
    main()