#include <bits/stdc++.h>
using namespace std;
int a[100005];
int dp[2505][2505];
string s, p;
int A[10005];
int main() {
  ios::sync_with_stdio(false);
  cin >> s >> p;
  for (int i = 0; i < s.size(); i++) {
    int k = 0;
    for (int j = i; j < s.size(); j++) {
      if (s[j] == p[k]) {
        k++;
        if (k == p.size()) {
          a[i] = (j - i) + 1;
          break;
        }
      }
    }
    if (!a[i]) a[i] = -1;
  }
  int Len_s = s.size();
  int Len_p = p.size();
  int x = p.size();
  for (int i = 0; i < s.size(); i++) {
    for (int j = 0; j <= i; j++) {
      dp[i + 1][j] = max(dp[i + 1][j], dp[i][j]);
      dp[i + 1][j + 1] = max(dp[i + 1][j + 1], dp[i][j]);
      if (a[i] >= 0) {
        dp[i + a[i]][j + (a[i] - x)] =
            max(dp[i + a[i]][j + (a[i] - x)], dp[i][j] + 1);
      }
    }
  }
  for (int j = 0; j <= s.size(); j++) {
    cout << dp[s.size()][j] << " ";
  }
  cout << endl;
}

### Prompt

Create a solution in cpp for the following problem:

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", ""}.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int a[100005];
int dp[2505][2505];
string s, p;
int A[10005];
int main() {
  ios::sync_with_stdio(false);
  cin >> s >> p;
  for (int i = 0; i < s.size(); i++) {
    int k = 0;
    for (int j = i; j < s.size(); j++) {
      if (s[j] == p[k]) {
        k++;
        if (k == p.size()) {
          a[i] = (j - i) + 1;
          break;
        }
      }
    }
    if (!a[i]) a[i] = -1;
  }
  int Len_s = s.size();
  int Len_p = p.size();
  int x = p.size();
  for (int i = 0; i < s.size(); i++) {
    for (int j = 0; j <= i; j++) {
      dp[i + 1][j] = max(dp[i + 1][j], dp[i][j]);
      dp[i + 1][j + 1] = max(dp[i + 1][j + 1], dp[i][j]);
      if (a[i] >= 0) {
        dp[i + a[i]][j + (a[i] - x)] =
            max(dp[i + a[i]][j + (a[i] - x)], dp[i][j] + 1);
      }
    }
  }
  for (int j = 0; j <= s.size(); j++) {
    cout << dp[s.size()][j] << " ";
  }
  cout << endl;
}

```