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 (7.3.0) (judge verdict: Accepted)

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

# ある余りを10倍して13で割ったときの余りへの変換表
rests = [0] * 13
for i in range(len(rests)):
  rests[i] = i * 10 % 13
  
dp = [[0] * 13 for i in range(len(S))]

x0 = S[0]
if x0 != "?":
  dp[0][int(x0)] = 1
else:
  # ?の場合は0～9を全て取ることができ、その余りは0～9となる
  for i in range(10):
    dp[0][i] = 1

for i in range(1, len(dp)):
  x = S[i]
  if x != "?":
    x = int(x)
    # ?じゃない場合は、直前の各あまりをrestsで変換して、その数を足したところに数を代入する
    for j in range(len(dp[i - 1])):
      dp[i][(rests[j] + x) % 13] += dp[i - 1][j]
      dp[i][(rests[j] + x) % 13] %= MOD
  else:
    # ?は0～9の全てを取ることができる
    for j in range(len(dp[i - 1])):
      for k in range(10):
        dp[i][(rests[j] + k) % 13] += dp[i - 1][j]
        dp[i][(rests[j] + k) % 13] %= MOD
  
print(dp[-1][5])