Champernowne Constant

Time limit8sMemory limit512 MB

Summary

For each query, print the K digits of the Champernowne constant starting at decimal position N, where integers are concatenated in order.

Level: Medium5 of 10
Topics: Math, String matching, Implementation
Solved: No attempts yet

Problem

The Champernowne constant is the irrational number whose decimal expansion is every positive integer written out in increasing order, concatenated after the decimal point. It begins like this.

$0.123456789101112\dots$

Given two natural numbers $N$ and $K$ , write a program that prints the $K$ digits of this constant starting at decimal place $N$ .

Input

The input has several lines. Each line holds two positive integers $N$ and $K$ separated by one space, with $N \le 10^9$ and $K \le 100$ .

The end of the input is a line holding two zeros. Do not process that line.

Output

For each line, print the $K$ digits on one line with no separators.

Examples5

Example 1
Input
```
4 5
6 7
0 0
```
Expected output
```
45678
6789101
```
Example 2
Input
```
1 1
1 2
9 1
10 1
11 1
0 0
```
Expected output
```
1
12
9
1
0
```

Example 3

Input

Expected output

Example 4

Input

1 100
0 0

Expected output

1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545

Example 5

Input

1000000000 100
0 0

Expected output

1234567901234567911234567921234567931234567941234567951234567961234567971234567981234567991234568001