Bar Codes
Description
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
Your program is to read from standard input. The first line 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
Your program is to write to standard output. On the first line your program should write the total number of symbols in BC(n,k,m). On each of the s following lines, it should write the rank of the corresponding symbol in the input.
7 4 3
5
1001110
1110110
1001100
1001110
100010016
4
15
3
4
0