#include <bits/stdc++.h>
using namespace std;
char s[2005], p[505];
int pre[2005], del[2005], dp[2005][2005];
int main() {
  scanf("%s%s", s + 1, p + 1);
  int n = strlen(s + 1), lenp = strlen(p + 1);
  memset(pre, -1, sizeof(pre));
  for (int i = lenp; i <= n; ++i) {
    int k = i, j = lenp;
    while (k >= 1 && j >= 1) {
      if (s[k] == p[j])
        --k, --j;
      else
        --k, ++del[i];
    }
    if (!j) pre[i] = k;
  }
  for (int i = 0; i <= n; ++i)
    for (int j = i + 1; j <= n; ++j) dp[i][j] = -0x3f3f3f3f;
  for (int i = 1; i <= n; ++i) {
    for (int j = 0; j <= i; ++j) {
      if (j) dp[i][j] = dp[i - 1][j - 1];
      dp[i][j] = max(dp[i][j], dp[i - 1][j]);
      if (pre[i] != -1 && j >= del[i])
        dp[i][j] = max(dp[i][j], dp[pre[i]][j - del[i]] + 1);
    }
  }
  for (int i = 0; i <= n; ++i) printf("%d ", dp[n][i]);
  return 0;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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;
char s[2005], p[505];
int pre[2005], del[2005], dp[2005][2005];
int main() {
  scanf("%s%s", s + 1, p + 1);
  int n = strlen(s + 1), lenp = strlen(p + 1);
  memset(pre, -1, sizeof(pre));
  for (int i = lenp; i <= n; ++i) {
    int k = i, j = lenp;
    while (k >= 1 && j >= 1) {
      if (s[k] == p[j])
        --k, --j;
      else
        --k, ++del[i];
    }
    if (!j) pre[i] = k;
  }
  for (int i = 0; i <= n; ++i)
    for (int j = i + 1; j <= n; ++j) dp[i][j] = -0x3f3f3f3f;
  for (int i = 1; i <= n; ++i) {
    for (int j = 0; j <= i; ++j) {
      if (j) dp[i][j] = dp[i - 1][j - 1];
      dp[i][j] = max(dp[i][j], dp[i - 1][j]);
      if (pre[i] != -1 && j >= del[i])
        dp[i][j] = max(dp[i][j], dp[pre[i]][j - del[i]] + 1);
    }
  }
  for (int i = 0; i <= n; ++i) printf("%d ", dp[n][i]);
  return 0;
}

```