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: Runtime Error)

cnt=0

def calcuration(i,A,B):
        global cnt
        if(A[i]=="?"):
                for k in range(10):
                        tmp=""
                        B[i]=k
                        if(i!=len(A)-1):
                                calcuration(i+1,A,B)
                        else:
                                for para2 in B:
                                        tmp+=str(para2)
                                tmp = int(tmp)
                                print(tmp)
                                if(tmp%13==5):
                                        #print("OK")
                                        cnt+=1
        else:
                if(i!=len(A)-1):
                        calcuration(i+1,A,B)
                else:
                        tmp=""
                        for para2 in B:
                                tmp+=str(para2)
                        tmp = int(tmp)
                        #print(tmp)
                        if(tmp%13==5):
                                #print("OK")
                                cnt+=1


A = list(input())
B = A[:]

for num,para in enumerate(B):
    if(para=="?"):
        B[num]=0

calcuration(0,A,B)

print(cnt%(10**9+7))