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()
MOD = 10**9+7
dp = [[0 for i in range(13)] for j in range(10**5+1)]
dp[0][0] = 1

for i in range(len(S)):
    s = S[i]
    if s == '?':
        for j in range(13):
            dp[i+1][j] = sum(dp[i])-dp[i][4-int((j+2)/3)]-dp[i][8-int((j+1)/3)]-dp[i][12-int(j/3)]
    else:
        for j in range(13):
            dp[i+1][(j*10+int(s))%13] += dp[i][j]
print(dp[len(S)][5]%MOD)