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", ""}.
#include <bits/stdc++.h>
using namespace std;
const int N = 2004;
int n, m, pos[N], f[N][N];
string s, p;
void init() {
  memset(pos, 0xff, sizeof pos);
  for (int i = m - 1; i < n; i++) {
    int j = i;
    for (int k = p.size() - 1; k >= 0; k--) {
      while (j >= 0 && s[j] != p[k]) j--;
      j--;
      if (j < -1) break;
    }
    pos[i] = j + 1;
  }
}
void maximize(int &a, int b) {
  if (a < b) a = b;
}
void process() {
  memset(f, 0xbf, sizeof f);
  f[0][0] = 0;
  for (int i = 1; i <= n; i++)
    for (int j = 0; j <= i; j++) {
      f[i][j] = f[i - 1][j];
      if (j) maximize(f[i][j], f[i - 1][j - 1]);
      if (pos[i - 1] != -1) {
        if (i - pos[i - 1] - m <= j)
          maximize(f[i][j], f[pos[i - 1]][j - (i - pos[i - 1] - m)] + 1);
      }
    }
  for (int i = 0; i <= n; i++) cout << f[n][i] << ' ';
}
int main() {
  ios::sync_with_stdio(false);
  cin >> s >> p;
  n = s.size();
  m = p.size();
  init();
  process();
}
