IOI '95 - Eindhoven, Netherlands

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: Four fences and some of their letter strings (joints not to scale)

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 Specification

The first line of input contains the numbers ~n~, ~k~, and ~m~ ~(1 \le n, k, m \le 33)~. On the second line is a number ~s~ ~(0 \le s \le 100)~. The following ~s~ lines each contain some symbol in ~BC(n, k, m)~, represented by 0s and 1s as in Figure 2.

Output Specification

On the first line of output, 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 (Subtask B).

Sample Input

7 4 3
5
1001110
1110110
1001100
1001110
1000100

Sample Output

16
4
15
3
4
0