#include <bits/stdc++.h>
using namespace std;
const int maxn = 2010;
const int maxm = 510;
char s[maxn], p[maxm];
int n, m;
int d[maxn][maxn];
int f[maxn];
int main() {
  scanf("%s%s", s, p);
  int n = strlen(s), m = strlen(p);
  for (int i = 0; i < n; i++) {
    int st = i, j;
    for (j = 0; j < m; j++) {
      while (st < n && s[st] != p[j]) ++st;
      if (st == n)
        break;
      else
        ++st;
    }
    if (j == m)
      f[i] = st - i;
    else
      f[i] = -1;
  }
  for (int i = 0; i < n; i++)
    for (int j = 0; j <= i; j++) {
      d[i + 1][j] = max(d[i + 1][j], d[i][j]);
      d[i + 1][j + 1] = max(d[i + 1][j + 1], d[i][j]);
      if (f[i] >= 0)
        d[i + f[i]][j + f[i] - m] = max(d[i + f[i]][j + f[i] - m], d[i][j] + 1);
    }
  for (int i = 0; i <= n; i++) printf("%d ", d[n][i]);
  printf("\n");
  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;
const int maxn = 2010;
const int maxm = 510;
char s[maxn], p[maxm];
int n, m;
int d[maxn][maxn];
int f[maxn];
int main() {
  scanf("%s%s", s, p);
  int n = strlen(s), m = strlen(p);
  for (int i = 0; i < n; i++) {
    int st = i, j;
    for (j = 0; j < m; j++) {
      while (st < n && s[st] != p[j]) ++st;
      if (st == n)
        break;
      else
        ++st;
    }
    if (j == m)
      f[i] = st - i;
    else
      f[i] = -1;
  }
  for (int i = 0; i < n; i++)
    for (int j = 0; j <= i; j++) {
      d[i + 1][j] = max(d[i + 1][j], d[i][j]);
      d[i + 1][j + 1] = max(d[i + 1][j + 1], d[i][j]);
      if (f[i] >= 0)
        d[i + f[i]][j + f[i] - m] = max(d[i + f[i]][j + f[i] - m], d[i][j] + 1);
    }
  for (int i = 0; i <= n; i++) printf("%d ", d[n][i]);
  printf("\n");
  return 0;
}

```