IOI'95 Task: Bar Codes

# Task: Bar Codes

A bar-code symbol consists of alternating dark and light bars, starting with a dark bar on the left. Each bar is a number of units wide. Figure 1 shows a bar-code symbol consisting of 4 bars that extend over 1+2+3+1=7 units. Figure 1: Bar-code symbol over 7 units (see top) with 4 bars (see bottom)

In general, the bar code BC(n,k,m) is the set of all symbols with k bars that together extend over exactly n units, each bar being at most m units wide. For instance, the symbol in Figure 1 belongs to BC(7,4,3) but not to BC(7,4,2).

```
0: 1000100  |  8: 1100100
1: 1000110  |  9: 1100110
2: 1001000  | 10: 1101000
3: 1001100  | 11: 1101100
4: 1001110  | 12: 1101110
5: 1011000  | 13: 1110010
6: 1011100  | 14: 1110100
7: 1100010  | 15: 1110110
```
Figure 2: All symbols of BC(7,4,3)

Figure 2 shows all 16 symbols in BC(7,4,3). Each `1' represents a dark unit, each `0' a light unit. The symbols appear in lexicographic (dictionary) order. The number on the left of the colon (`:') is the rank of the symbol. The symbol in Figure 1 has rank 4 in BC(7,4,3).

## Input Data

The first line of file INPUT.TXT contains the numbers n, k, and m (1<=n,k,m<=33). On the second line is a number s (0<=s<=100). The following s lines each contain some symbol in BC(n,k,m), represented by `0's and `1's as in Figure 2.

## Output Data

On the first line of file OUTPUT.TXT your program should write the total number of symbols in BC(n,k,m) (Subtask A). On each of the s following lines, it should write the rank of the corresponding symbol in the input file (Subtask B).

## Example Input and Output

Figure 3 gives possible input and output files for the example above.
```
____________   _____________
|INPUT.TXT |   |OUTPUT.TXT |
|__________|   |___________|
|7 4 3     |   |16         |
|5         |   |4          |
|1001110   |   |15         |
|1110110   |   |3          |
|1001100   |   |4          |
|1001110   |   |0          |
|1000100   |   |___________|
|__________|
```
Figure 3: Example input and output

IOI 95