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)

import sys
readline = sys.stdin.readline

def main():

	#s = tuple(input())
	s = input()
	length = len(s)

	dp = [[0]*13 for _ in range(length)]
	MOD = 10**9+7
	if s[-1] == '?':
		for i in range(10):
			dp[0][i] = 1
	else:
		dp[0][int(s[-1])] = 1

	for i in range(1,length):
		if s[-i-1] != '?':
			num = (int(s[-i-1]) * (10**i)) % 13
			for j in range(13):
				dp[i][j] = dp[i-1][(13-num+j)%13]
				dp[i][j] %= MOD
		else:
			num = (10**i) % 13
			a = 0
			for j in range(10):
				for k in range(13):
					dp[i][k] += dp[i-1][(13-a+k)%13]
					dp[i][k] %= MOD
				a += num

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

if __name__ == '__main__':
	main()