Digit frequency

Interview

Time limit2sMemory limit512 MB

Summary

Count how many times a given digit d appears when writing every integer from 1 to n.

Level: Easy3 of 10
Topics: Math, Implementation
Solved: No attempts yet

Problem

Write down every integer from 1 to $n$ in order. Write a program that counts how many times the single digit $d$ appears in what you wrote.

For example, with $n = 11$ and $d = 1$ you write 1 2 3 4 5 6 7 8 9 10 11. The digit 1 appears once in 1, once in 10, and twice in 11, so its frequency is 4.

Input

The first line contains a natural number $n$ ( $1 \le n \le 100000$ ) and a single digit $d$ ( $0 \le d \le 9$ ), separated by one space.

Output

Print on the first line how many times the digit $d$ appears across all the numbers written from 1 to $n$ .

Examples2

Example 1
Input
```
11 1
```
Expected output
```
4
```
Example 2
Input
```
100 3
```
Expected output
```
20
```