The Counting Problem

Time limit1sMemory limit128 MB

Summary

For each pair (a, b), count how many times each digit 0 through 9 appears when writing every integer between them, inclusive.

Level: Medium6 of 10
Topics: Math, Implementation, Brute force, Recursion
Solved: No attempts yet

Problem

You are given two integers $a$ and $b$ . List every integer between $a$ and $b$ , inclusive, and count how many times each digit (0 through 9) appears across the whole list.

For example, if $a = 1024$ and $b = 1032$ , the list is

1024 1025 1026 1027 1028 1029 1030 1031 1032

which contains the digit 0 ten times, the digit 1 ten times, the digit 2 seven times, the digit 3 three times, and so on.

The order of $a$ and $b$ is not fixed: $a$ may be greater than $b$ , and in that case you still count every integer between the two values.

Input

The input consists of up to 500 lines. Each line contains two integers $a$ and $b$ with $0 < a, b < 100{,}000{,}000$ . The input is terminated by a line containing 0 0, which is not part of the input.

Output

For each input line, print one line with ten integers separated by single spaces. The first integer is the number of occurrences of the digit 0, the second is the number of occurrences of the digit 1, and so on, up to the tenth integer, which is the number of occurrences of the digit 9.

Examples3

Example 1

Input

Expected output

1 2 1 1 1 1 1 1 1 1
85 185 185 185 190 96 96 96 95 93
40 40 40 93 136 82 40 40 40 40
115 666 215 215 214 205 205 154 105 106
16 113 19 20 114 20 20 19 19 16
107 105 100 101 101 197 200 200 200 200
413 1133 503 503 503 502 502 417 402 412
196 512 186 104 87 93 97 97 142 196
398 1375 398 398 405 499 499 495 488 471
294 1256 296 296 296 296 287 286 286 247

Example 2
Input
```
1 1
0 0
```
Expected output
```
0 1 0 0 0 0 0 0 0 0
```
Example 3
Input
```
10 1
0 0
```
Expected output
```
1 2 1 1 1 1 1 1 1 1
```