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()
N = len(S)
mod = 10**9+7
P = 13
 
dp = [[0 for _ in range(P)] for _ in range(N)]
 
# 1桁目だけ事前計算
if S[N-1] == '?':
    tmp = [0 for _ in range(P)]
    for i in range(10):
        tmp[i % P] = 1
    dp[0] = tmp
else:
    dp[0][int(S[N-1]) % P] = 1
 
for i in range(1, N):
    k = N-i-1
    if S[k] == '?':
        base = pow(10, i, P)
        for j in range(10):
            r = base*j % P
            for m in range(P):
                dp[i][(m+r)%P] = (dp[i][(m+r)%P] + dp[i-1][m]) % mod
    else:
        r = pow(10, i, P) * int(S[k]) % P
        for j in range(P):
            dp[i][(j+r)%P] = max(dp[i][(j+r)%P], dp[i-1][j])
 
print(dp[-1][5])