#include <bits/stdc++.h>
using namespace std;
string s, p;
int n, m, dp[2005][2005], a[2005];
int main() {
  int i, j, k;
  cin >> s >> p;
  n = s.length();
  m = p.length();
  for (i = 0; i < (n); i++) {
    j = i;
    k = 0;
    while (j < n && k < m) {
      if (s[j] == p[k]) k++;
      j++;
    }
    if (k == m)
      a[i] = j - i;
    else
      a[i] = -1;
  }
  for (i = 0; i < (n); i++) {
    for (j = 0; j < (i + 1); 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] != -1)
        dp[i + a[i]][j + a[i] - m] =
            max(dp[i + a[i]][j + a[i] - m], dp[i][j] + 1);
    }
  }
  for (i = 0; i < (n + 1); i++) cout << dp[n][i] << " ";
  cout << endl;
  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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;
string s, p;
int n, m, dp[2005][2005], a[2005];
int main() {
  int i, j, k;
  cin >> s >> p;
  n = s.length();
  m = p.length();
  for (i = 0; i < (n); i++) {
    j = i;
    k = 0;
    while (j < n && k < m) {
      if (s[j] == p[k]) k++;
      j++;
    }
    if (k == m)
      a[i] = j - i;
    else
      a[i] = -1;
  }
  for (i = 0; i < (n); i++) {
    for (j = 0; j < (i + 1); 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] != -1)
        dp[i + a[i]][j + a[i] - m] =
            max(dp[i + a[i]][j + a[i] - m], dp[i][j] + 1);
    }
  }
  for (i = 0; i < (n + 1); i++) cout << dp[n][i] << " ";
  cout << endl;
  return 0;
}

```