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.util.*;
import java.io.*;

public class Main{

    BufferedReader in;
    StringTokenizer str = null;
    PrintWriter out;

    private String next() throws Exception{
    	while (str == null || !str.hasMoreElements())
    	    str = new StringTokenizer(in.readLine());
    	return str.nextToken();
    }
    
    private int nextInt() throws Exception{
	   return Integer.parseInt(next());
    }
    
    public void run() throws Exception{
    	in = new BufferedReader(new InputStreamReader(System.in));
    	out = new PrintWriter(System.out);
        char []s = next().toCharArray(), t = next().toCharArray();
        int n = s.length, m = t.length;
        int []a = new int[n];
        Arrays.fill(a, -1);
        for(int i = 0; i < n; ++i){
            int at = i;
            for(int j = m - 1; j >= 0; --j) {
                while(at >= 0 && s[at] != t[j]) {
                    --at;
                }
                --at;
            }
            if (at >= -1) {
                a[i] = i - at;
            }
        }

        // System.out.println(Arrays.toString(a));

        int [][]dp = new int[n + 1][n + 1];
        for(int []i : dp) Arrays.fill(i, -1);
        dp[0][0] = 0;
        for(int i = 1; i <= n; ++i) {
            for(int j = 0; j <= i; ++j) {
                dp[i][j] = dp[i-1][j];
                if (j > 0 && dp[i-1][j-1] >= 0) dp[i][j] = Math.max(dp[i][j], dp[i-1][j-1]);
                if (a[i-1] != -1){
                    if (j - a[i-1] + m >= 0 && dp[i-a[i-1]][j-a[i-1]+m] >= 0) {
                        dp[i][j] = Math.max(dp[i][j], dp[i-a[i-1]][j-a[i-1]+m] + 1);    
                    }
                }
            }
        }
        // for(int i = 0; i <= n; ++i) {
        //     System.out.println(Arrays.toString(dp[i]));
        // }
        for(int i = 0; i <= n; ++i) {
            out.print(dp[n][i] + " ");
        }
        out.println();
        out.close();
    }

    public static void main(String args[]) throws Exception{
	   new Main().run();
    }
}