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 static java.lang.Math.*;
import java.util.*;
import java.util.function.*;
import java.lang.*;

public class Main {
    final static boolean debug = false;
    final static String fileName = "";
    final static boolean useFiles = false;

    public static void main(String[] args) throws FileNotFoundException {
        long start;
        if (debug)
            start = System.nanoTime();
        InputStream inputStream;
        OutputStream outputStream;
        if (useFiles) {
            inputStream = new FileInputStream(fileName + ".in");
            outputStream = new FileOutputStream(fileName + ".out");
        } else {
            inputStream = System.in;
            outputStream = System.out;
        }
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task(in, out);
        solver.solve();
        if(debug)
            out.println((System.nanoTime() - start) / 1e+9);
        out.close();
    }
}

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 double nextDouble() {
        return Double.parseDouble(next());
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

    public byte nextByte() {
        return Byte.parseByte(next());
    }

    public char nextChar() {
        return next().charAt(0);
    }

    public byte[][] nextBitMatrix(int n, int m) {
        byte[][] a = new byte[n][m];
        for (int i = 0; i < n; i++) {
            String s = next();
            for (int j = 0; j < m; j++) {
                a[i][j] = (byte) (s.charAt(j) - '0');
            }
        }
        return a;
    }

    public char[][] nextCharMatrix(int n, int m) {
        char[][] a = new char[n][m];
        for (int i = 0; i < n; i++) {
            String s = next();
            for (int j = 0; j < m; j++) {
                a[i][j] = s.charAt(j);
            }
        }
        return a;
    }

    public int[] nextIntArray(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = nextInt();
        return a;
    }

    public long[] nextLongArray(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = nextLong();
        return a;
    }
}

class Task {
    public void solve() {
        char[] s = in.next().toCharArray();
        char[] p = in.next().toCharArray();
        int n = s.length;
        int m = p.length;
        int[] next = new int[n];
        for (int i = 0; i < n; i++) {
            int j = 0, k = i;
            for (; k < n && j < m; k++) {
                if (p[j] == s[k])
                    j++;
            }
            if (j == m)
                next[i] = k;
            else
                next[i] = -1;
        }
        final int maxResult = n / m;
        int[][] d = new int[n + 1][maxResult + 1];
        for (int i = 1; i <= maxResult; i++) {
            d[n][i] = (int)1e9;
        }
        d[n][0] = 0;
        for (int i = n - 1; i >= 0; i--) {
            d[i][0] = 0;
            for (int j = 1; j <= maxResult; j++) {
                d[i][j] = d[i + 1][j];
                if (next[i] != -1)
                    d[i][j] = min(d[i][j], d[next[i]][j - 1] + (next[i] - i - m));
            }
        }
        int[] result = new int[n + 1];
        for (int ans = 1; ans <= maxResult; ans++) {
            for (int i = d[0][ans]; i <= n - ans * m; i++) {
                result[i] = max(result[i], ans);
            }
        }
        for (int i = 0; i <= n; i++) {
            out.print(result[i] + " ");
        }
        out.println();
    }

    private InputReader in;
    private PrintWriter out;

    Task(InputReader in, PrintWriter out) {
        this.in = in;
        this.out = out;
    }
}
