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: Wrong Answer)

import math
S=input()
dp=[0]*13
dp[0]=1
# dp[k] 13で割った余りkのパターン数
mod = 1000000007

for i in range(len(S)):
    nextDp=[0]*13
    if S[i] == "?":
        for j in range(13):
            for k in range(10):
                nextDp[((10*j) + k) % 13] += dp[j]
                nextDp[((10*j) + k) % 13] %= mod
    else:
        k = int(S[i])
        for j in range(13):
            nextDp[((10*j) + k) % 13] += dp[j]
            nextDp[((10*j) + k) % 13] %= mod
    for j in range(13):
        dp[j] = nextDp[j]
    print(dp)

print(dp[5])