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.BufferedInputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.LinkedList;
import java.util.Map.Entry;
import java.util.Queue;
import java.util.Set;
import java.util.TreeSet;

public class Main
{
	public void foo()
	{
		MyScanner scan = new MyScanner();
		char[] s = scan.next().toCharArray();
		char[] p = scan.next().toCharArray();
		int n = s.length;
		int m = p.length;
		int[] a = new int[n + 1];
		for(int i = m;i <= n;++i)
		{
			int j = i -1;
			int k = m - 1;
			while(j >= 0 && k >= 0)
			{
				if(s[j] == p[k])
				{
					--k;
				}
				--j;
			}
			if(k < 0)
			{
				a[i] = i - j - 1;
			}
		}
		int[][] dp = new int[n + 1][n + 1];
		for(int i = 0;i <= n;++i)
		{
			Arrays.fill(dp[i], -1);
		}
		dp[0][0] = 0;
		for(int i = 1;i <= n;++i)
		{
			dp[i][0] = dp[i - 1][0];
			if(a[i] == m)
			{
				dp[i][0] = Math.max(dp[i][0], dp[i - m][0] + 1);
			}
		}
		for(int i = 1;i <= n;++i)
		{
			for(int j = 1;j <= i;++j)
			{
				dp[i][j] = Math.max(dp[i - 1][j - 1], dp[i - 1][j]);
				if(a[i] > 0 && a[i] - m <= j)
				{
					dp[i][j] = Math.max(dp[i][j], dp[i - a[i]][j - (a[i] - m)] + 1);
				}
			}
		}
		StringBuilder str = new StringBuilder();
		for(int i = 0;i <= n;++i)
		{
			str.append(dp[n][i] + " ");
		}
		System.out.println(str);
	}

	public static void main(String[] args)
	{
		new Main().foo();
	}
	
	class MyScanner
	{
	    private byte[] buf = new byte[1024];
	    private int curChar;
	    private int numChars;
	    BufferedInputStream bis = new BufferedInputStream(System.in);

	    public int read() 
	    {
	        if (-1 == numChars)
	        {
	        	throw new InputMismatchException();
	        }
	        if (curChar >= numChars)
	        {
	            curChar = 0;
	            try 
	            {
	                numChars = bis.read(buf);
	            }
	            catch (IOException e)
	            {
	                throw new InputMismatchException();
	            }
	            if (numChars <= 0)
	            {
	            	return -1;
	            }
	        }
	        return buf[curChar++];
	    }

	    public int nextInt() 
	    {
	        int c = read();
	        while (isSpaceChar(c))
	        {
	        	c = read();
	        }
	        int sgn = 1;
	        if (c == '-') 
	        {
	            sgn = -1;
	            c = read();
	        }
	        int res = 0;
	        do 
	        {
	            if (c < '0' || c > '9')
	            {
	            	throw new InputMismatchException();
	            }
	            res *= 10;
	            res += c - '0';
	            c = read();
	        } while (!isSpaceChar(c));
	        return res * sgn;
	    }
	    
	    public long nextLong() 
	    {
	    	int c = read();
	    	while (isSpaceChar(c))
	    	{
	    		c = read();
	    	}
	    	int sgn = 1;
	    	if (c == '-') 
	    	{
	    		sgn = -1;
	    		c = read();
	    	}
	    	long res = 0;
	    	do 
	    	{
	    		if (c < '0' || c > '9')
	    		{
	    			throw new InputMismatchException();
	    		}
	    		res *= 10;
	    		res += c - '0';
	    		c = read();
	    	} while (!isSpaceChar(c));
	    	return res * sgn;
	    }
	    
	    public String next()
	    {
	        int c = read();
	        while (isSpaceChar(c))
	        {
	        	c = read();
	        }
	        StringBuilder res = new StringBuilder();
	        do 
	        {
	            res.appendCodePoint(c);
	            c = read();
	        } while (!isSpaceChar(c));
	        return res.toString();
	    }

	    private boolean isSpaceChar(int c) 
	    {
	        return ' ' == c || '\n' == c || '\r' == c || '\t' == c || -1 == c;
	    }
	}
}