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)

s = input()
dp = [[0 for i in range(13)] for i in range(len(s))]
if s[-1] != "?":
    dp[0][int(s[-1]) % 13] += 1
else:
    for k in range(10):
        dp[0][k % 13] += 1
d = [1]
for i in range(1,len(s)):
    d.append(d[i-1]*10 % 13)
    
for i in range(1,len(s)):
    for r in range(13):
        if s[-(i+1)] == "?":
            for k in range(10): 
                dp[i][(k * d[i] + r) % 13] += dp[i-1][r]
                
        else:
            dp[i][(int(s[-(i+1)]) * d[i] + r) % 13] += dp[i-1][r]
    for r in range(13):
        dp[i][r]  %= 10**9 + 7
print(dp[len(s)-1][5]%(10**9+7))