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)

MOD = (10**9) + 7

s = input().rstrip()

keta_all = len(s)
amari_cnt_old = [1] + [0] * 12

for i,a in enumerate(s):
	keta_cur = keta_all - i-1
	amari_cnt_new = [0] * 13
	
	if a == "?":
		for j in range(10):
			amari_cur = (j * (10**keta_cur))%13
			for amari_old,amari_cnt_tmp in enumerate(amari_cnt_old):
				amari_cnt_new[(amari_cur+amari_old)%13] += (amari_cnt_tmp%MOD)
	else:
		amari_cur = ((int(a)) * (10**keta_cur))%13
		for amari_old,amari_cnt_tmp in enumerate(amari_cnt_old):
			amari_cnt_new[(amari_cur+amari_old)%13] += (amari_cnt_tmp%MOD)
	
	amari_cnt_old = amari_cnt_new

print((amari_cnt_old[5]%MOD))