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.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;

public class CF272C {
    public static void main(String[] args) throws Exception {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        char[] s = in.readLine().toCharArray();
        char[] p = in.readLine().toCharArray();

        int[][] next = new int[s.length][];
        int[] last = new int[26];
        Arrays.fill(last, -1);
        for (int i = s.length - 1; i >= 0; i--) {
            last[s[i] - 'a'] = i;
            next[i] = last.clone();
        }
        int[] jump = new int[s.length];
        for (int i = 0; i < s.length; i++) {
            int at = i;
            int count = 0;
            for (int j = 0; j < p.length && at != -1 && at < s.length
                    && next[at][p[j] - 'a'] != -1; j++) {
                at = next[at][p[j] - 'a'] + 1;
                count++;
            }
            if (count == p.length)
                jump[i] = at;
            else
                jump[i] = -1;
        }
        int[][] dp = new int[s.length + 1][s.length + 1];
        for (int[] a : dp)
            Arrays.fill(a, Integer.MIN_VALUE);
        dp[0][0] = 0;
        for (int i = 0; i < s.length; i++) {
            for (int j = 0; j < s.length; j++) {
                dp[i + 1][j] = Math.max(dp[i][j], dp[i + 1][j]);
                dp[i + 1][j + 1] = Math.max(dp[i + 1][j + 1], dp[i][j]);
                if (jump[i] != -1 && jump[i] - i - p.length + j <= s.length)
                    dp[jump[i]][j + jump[i] - i - p.length] = Math.max(
                            dp[jump[i]][j + (jump[i] - i) - p.length],
                            dp[i][j] + 1);
            }
        }
        for (int i = 0; i <= s.length; i++)
            System.out.print(dp[s.length][i] + " ");
    }
}
