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: Accepted)


S = input()

MOD = 10 ** 9 + 7
count = 0
S_len = len(S)

dp = [[0 for i in range(13)] for j in range(100006)]
c = -1
if S[0] != '?':
    c = int(S[0])
for j in range(10):
    if c == -1:
        dp[1][j] = 1
    else:
        dp[1][c] = 1

for i in range(2, S_len + 1):
    c = -1
    if S[i - 1] != '?':
        c = ord(S[i - 1]) - ord('0')

    for j in range(10):
        if c != -1 and c != j:
            continue
        for k in range(13):
            dp[i][(k * 10 + j) % 13] += dp[i - 1][k] % MOD


print(dp[S_len][5] % MOD)