Dreamoon has a string s and a pattern string p. He first removes exactly x characters from s obtaining string s' as a result. Then he calculates <image> that is defined as the maximal number of non-overlapping substrings equal to p that can be found in s'. He wants to make this number as big as possible.

More formally, let's define <image> as maximum value of <image> over all s' that can be obtained by removing exactly x characters from s. Dreamoon wants to know <image> for all x from 0 to |s| where |s| denotes the length of string s.

Input

The first line of the input contains the string s (1 ≤ |s| ≤ 2 000).

The second line of the input contains the string p (1 ≤ |p| ≤ 500).

Both strings will only consist of lower case English letters.

Output

Print |s| + 1 space-separated integers in a single line representing the <image> for all x from 0 to |s|.

Examples

Input

aaaaa
aa


Output

2 2 1 1 0 0


Input

axbaxxb
ab


Output

0 1 1 2 1 1 0 0

Note

For the first sample, the corresponding optimal values of s' after removal 0 through |s| = 5 characters from s are {"aaaaa", "aaaa", "aaa", "aa", "a", ""}. 

For the second sample, possible corresponding optimal values of s' are {"axbaxxb", "abaxxb", "axbab", "abab", "aba", "ab", "a", ""}.
import java.io.*;
import java.util.*;


public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskE solver = new TaskE();
        solver.solve(in, out);
        out.close();
    }
}


class TaskE {

    public void solve(InputReader in, OutputWriter out) {

        String text = in.next();
        String pattern = in.next();

        int minLengths[] = calculateMinLengths(text, pattern);
        int DP[][] = createDPTab(text, pattern);
        int n = text.length();
        int m = pattern.length();

        for (int i = 0; i < n; i++) {
            for (int j = 0; j <= i; j++) {
                if(valid(i+1,j,n)) {
                    DP[i+1][j] = Math.max(DP[i+1][j], DP[i][j]);
                }
                if(valid(i+1,j+1,n)) {
                    DP[i+1][j+1] = Math.max(DP[i+1][j+1], DP[i][j]);
                }
                if(valid(i+minLengths[i], j + minLengths[i] - pattern.length(),n)) {
                    DP[i+minLengths[i]][j+minLengths[i] - pattern.length()] = Math.max(DP[i+minLengths[i]][j+minLengths[i] - pattern.length()], DP[i][j] + 1);

                }
            }
        }
        for (int i = 0; i <= n; i++) {
            out.print(DP[n][i]+" ");
        }

    }

    private boolean valid(int i, int j, int n) {
        return (i>= 0 && i <= n && j>=0 && j <= n);
    }

    private int[][] createDPTab(String text, String pattern) {
        int n = text.length();
        int tab[][] = new int[n+1][n+1];
        for (int i = 0; i <= n; i++) {
            for (int j = 0; j <= n; j++) {
                tab[i][j] = 0;
            }
        }
        return tab;
    }

    private int[] calculateMinLengths(String text, String pattern) {
        int n = text.length();
        int m = pattern.length();
        int minLengths[] = new int[n+1];

        for (int i = 0; i <= n; i++) {
            int j = i;
            int k = 0;
            int counter = 0;
            while(j < n && k < m && counter < m) {
                if(text.charAt(j) == pattern.charAt(k)) {
                    k++;
                    counter++;
                }
                j++;
            }
            minLengths[i] = (counter == m) ? j - i : -1;
        }
        return minLengths;
    }



}

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }
    public long nextLong() {
        return Long.parseLong(next());
    }

}

class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public OutputWriter(Writer writer) {
        this.writer = new PrintWriter(writer);
    }

    public void print(Object... objects) {
        for (int i = 0; i < objects.length; i++) {
            if (i != 0) {
                writer.print(' ');
            }
            writer.print(objects[i]);
        }
    }

    public void printLine(Object... objects) {
        print(objects);
        writer.println();
    }

    public void close() {
        writer.close();
    }

}