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 sys
sys.setrecursionlimit(10 ** 7)
read = sys.stdin.buffer.read 
inp = sys.stdin.buffer.readline
def inpS(): return inp().rstrip().decode()
readlines = sys.stdin.buffer.readlines 
MOD = 10**9+7

S = inpS()
N = len(S)
dp=[[0]*13 for i in range(N+1)]
mul = 1
dp[0][0] = 1 # 余り0は1個
for i in range(N):
  if S[N-i-1] == "?":
    for dgt in range(10):
      for mo in range(13):
        ind = (dgt*mul+mo)%13
        dp[i+1][ind] += dp[i][mo]
        dp[i+1][ind] %= MOD
  else:
    s = int(S[N-i-1])
    for mo in range(13):
      ind = (s*mul+mo)%13
      dp[i+1][ind] += dp[i][mo]
      dp[i+1][ind] %= MOD
  mul *= 10
  mul %= MOD
print(dp[N][5])