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
N=13

dp=[0]*N
dp[0] = 1

mul = 1
for c in S[::-1]:
    next_dp=[0]*N
    
    for i in range(N):
        if c=='?':
            for j in range(10):
                ii = (i + (int(j)*mul)) % N
                next_dp[ii] += dp[i]
                next_dp[ii] = next_dp[ii] % MOD
        else:
            ii = (i + (int(c)*mul)) % N
            next_dp[ii] += dp[i]
            next_dp[ii] = next_dp[ii] % MOD

    mul *= 10
    dp = next_dp

print(dp[5])