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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

S=input()
keta=len(S)
dp=[[0 for j in range(13)] for i in range(keta)]
DIV=10**9+7

if S[-1]=="?":
  for i in range(10):
    dp[0][i]=1
else:
  dp[0][int(S[-1])]=1
  
def convert(bef,add):
  nex=bef+add
  if nex>=13:
    nex-=13
  return nex
  
for i in range(1,keta):
  if S[keta-1-i]=="?":
    for j in range(13):
      for k in range(10):
        dp[i][convert(j,k*(10**i)%13)]+=dp[i-1][j]
        dp[i][convert(j,k*(10**i)%13)]%=DIV
  else:
    ch=int(S[keta-1-i])
    for j in range(13):
      dp[i][convert(j,ch*(10**i)%13)]+=dp[i-1][j]
      dp[i][convert(j,ch*(10**i)%13)]%=DIV

print(dp[len(dp)-1][5])