#include <bits/stdc++.h>
const int maxn = 2222;
using namespace std;
char s1[maxn], s2[maxn];
int dp[maxn][maxn];
int n, m;
int solve(int i) {
  int top = m;
  int rq = 0;
  if (i < m) return maxn;
  while (top && i) {
    if (s1[i] == s2[top])
      top--;
    else
      rq++;
    i--;
  }
  if (top)
    return maxn;
  else
    return rq;
}
int main() {
  scanf("%s%s", s1 + 1, s2 + 1);
  n = strlen(s1 + 1);
  m = strlen(s2 + 1);
  for (int i = 0; i <= n; i++)
    for (int j = i + 1; j <= n; j++) dp[i][j] = -maxn;
  for (int i = 1; i <= n; i++) {
    int k = solve(i);
    for (int j = 0; j <= i; j++) {
      dp[i][j] = max(dp[i - 1][j], dp[i][j]);
      if (j >= k) {
        dp[i][j] = max(dp[i][j], dp[i - m - k][j - k] + 1);
      }
    }
  }
  for (int i = 0; i <= n; i++) {
    printf("%d ", dp[n][i]);
  }
  return 0;
}

### Prompt

In CPP, your task is to solve 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>
const int maxn = 2222;
using namespace std;
char s1[maxn], s2[maxn];
int dp[maxn][maxn];
int n, m;
int solve(int i) {
  int top = m;
  int rq = 0;
  if (i < m) return maxn;
  while (top && i) {
    if (s1[i] == s2[top])
      top--;
    else
      rq++;
    i--;
  }
  if (top)
    return maxn;
  else
    return rq;
}
int main() {
  scanf("%s%s", s1 + 1, s2 + 1);
  n = strlen(s1 + 1);
  m = strlen(s2 + 1);
  for (int i = 0; i <= n; i++)
    for (int j = i + 1; j <= n; j++) dp[i][j] = -maxn;
  for (int i = 1; i <= n; i++) {
    int k = solve(i);
    for (int j = 0; j <= i; j++) {
      dp[i][j] = max(dp[i - 1][j], dp[i][j]);
      if (j >= k) {
        dp[i][j] = max(dp[i][j], dp[i - m - k][j - k] + 1);
      }
    }
  }
  for (int i = 0; i <= n; i++) {
    printf("%d ", dp[n][i]);
  }
  return 0;
}

```