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: Time Limit Exceeded)

#!/usr/bin/env python3
import sys

MOD = 1000000007  # type: int

def solve(S: str):
    N = len(S)
    dp = [[0 for _ in range(13)] for _ in range(len(S))]
    if S[N-1] != '?':
        dp[0][int(S[N-1])] = 1
    else:
        dp[0] = [1,1,1,1,1,1,1,1,1,1,0,0,0]
    ten = [1]
    for i in range(1, len(S)):
        ten.append(ten[-1] * 10 % 13)
        ii = len(S) - i - 1
        for j in range(13):
            if S[ii] == '?':
                for ll in range(10):
                    kk = ll * ten[i] % 13
                    dp[i][j] += dp[i-1][(13 + j - kk)%13]
                    dp[i][j] %= MOD
            else:
                x = int(S[ii])
                m = x * ten[i] % 13
                dp[i][j] = dp[i-1][(13+j-m)%13]
                dp[i][j] %= MOD
    print(dp[len(S)-1][5])
    return


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    S = next(tokens)  # type: str
    solve(S)

if __name__ == '__main__':
    main()