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 = list(input())
MOD = 10 ** 9 + 7

DP = [[0] * 13 for _ in range(len(S))]

if S[-1] == "?":
  for i in range(10):
    DP[0][i] = 1
else:
  t = int(S[-1])
  DP[0][t] = 1

kk = 10
for i in range(1, len(S)):
  k = kk % 13
  if S[-1 - i] == "?":
    for t in range(10):
      for j in range(13):
        DP[i][(j + k * t) % 13] += DP[i - 1][j]
        DP[i][(j + k * t) % 13] %= MOD
  else:
    t = int(S[-1 - i])
    for j in range(13):
      DP[i][(j + k * t) % 13] = DP[i - 1][j]
  kk = kk * 10 % 13

print(DP[-1][5])