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", ""}.
#include <bits/stdc++.h>
using namespace std;
string s;
string p;
int a[2005];
int A[2005];
int ans[2005];
int dp[2005][2005];
int main() {
  cin >> s >> p;
  memset(a, -1, sizeof(a));
  a[0] = 0;
  for (int i = 0; i < s.size(); i++) {
    for (int j = p.size() - 1; j >= 0; j--) {
      if (s[i] == p[j]) a[j + 1] = a[j];
    }
    a[0] = i + 1;
    A[i + 1] = a[p.size()];
  }
  for (int i = 1; i <= s.size(); i++) {
    for (int j = 0; j <= i; j++) {
      dp[i][j] = dp[i - 1][j];
      if (A[i] >= 0 && j - (i - A[i] - p.size()) >= 0 &&
          j - (i - A[i] - p.size()) <= A[i])
        dp[i][j] = max(dp[A[i]][j - (i - A[i] - p.size())] + 1, dp[i][j]);
    }
  }
  for (int i = 0; i <= s.size(); i++) ans[i] = dp[s.size()][i];
  for (int i = 0; i <= s.size(); i++) cout << ans[i] << " ";
  return 0;
}
