Kattis

# Powers of 2

Powers of 2

Theta has been learning about powers of $2$ in school. She notices that some numbers when written out contain powers of $2$ in their digit representation: for instance, $12\, 560$ contains $256$ which is a power of $2$. She has been wondering how many such numbers there are.

Can you write a program that counts how many numbers contain a given power of $2$?

## Input

The input consists of a single line with two integers $n$ and $e$ ($0 \le n \le 9 \cdot 10^{18}, 0 \le e \le 62$).

## Output

Output a single integer that is equal to the number of distinct integers $k$ ($0 \le k \le n$) whose decimal representation contains the digits of $2^ e$ as a substring.

Sample Input 1 Sample Output 1
1000000 1

468559

Sample Input 2 Sample Output 2
1000000 5

49401

Sample Input 3 Sample Output 3
1000000 16

20

Sample Input 4 Sample Output 4
9000000000000000000 62

1

Sample Input 5 Sample Output 5
5432123456789876543 33

4842258985