description: The Winter holiday will be here soon. Mr. Chanek wants to decorate his house's wall with ornaments. The wall can be represented as a binary string a of length n. His favorite nephew has another binary string b of length m (m ≤ n).
  
  Mr. Chanek's nephew loves the non-negative integer k. His nephew wants exactly k occurrences of b as substrings in a. 
  
  However, Mr. Chanek does not know the value of k. So, for each k (0 ≤ k ≤ n - m + 1), find the minimum number of elements in a that have to be changed such that there are exactly k occurrences of b in a.
  
  A string s occurs exactly k times in t if there are exactly k different pairs (p,q) such that we can obtain s by deleting p characters from the beginning and q characters from the end of t.
  
  Input
  
  The first line contains two integers n and m (1 ≤ m ≤ n ≤ 500) — size of the binary string a and b respectively.
  
  The second line contains a binary string a of length n.
  
  The third line contains a binary string b of length m.
  
  Output
  
  Output n - m + 2 integers — the (k+1)-th integer denotes the minimal number of elements in a that have to be changed so there are exactly k occurrences of b as a substring in a.
  
  Example
  
  Input
  
  
  9 3
  100101011
  101
  
  
  Output
  
  
  1 1 0 1 6 -1 -1 -1
  
  Note
  
  For k = 0, to make the string a have no occurrence of 101, you can do one character change as follows.
  
  100101011 → 100100011
  
  For k = 1, you can also change a single character.
  
  100101011 → 100001011
  
  For k = 2, no changes are needed.
solution: #include <bits/stdc++.h>
  using namespace std;
  vector<long long int> prefix_function(string s) {
    long long int n = (long long int)s.length();
    vector<long long int> pi(n);
    for (long long int i = 1; i < n; i++) {
      long long int j = pi[i - 1];
      while (j > 0 && s[i] != s[j]) j = pi[j - 1];
      if (s[i] == s[j]) j++;
      pi[i] = j;
    }
    return pi;
  }
  void compute_automaton(string s, vector<vector<long long int>>& aut) {
    s += '#';
    long long int n = s.size();
    vector<long long int> pi = prefix_function(s);
    aut.assign(n, vector<long long int>(2));
    for (long long int i = 0; i < n; i++) {
      for (long long int c = 0; c < 2; c++) {
        if (i > 0 && '0' + c != s[i])
          aut[i][c] = aut[pi[i - 1]][c];
        else
          aut[i][c] = i + ('0' + c == s[i]);
      }
    }
  }
  long long int dp[505][505];
  long long int inf = 1000000000;
  signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    long long int n, m;
    cin >> n >> m;
    string a, b;
    cin >> a >> b;
    vector<vector<long long int>> aut;
    compute_automaton(b, aut);
    for (long long int i = 0; i <= 500; i++) {
      for (long long int j = 0; j <= m; j++) {
        dp[i][j] = inf;
      }
    }
    dp[0][0] = 0;
    for (long long int i = 0; i < n; i++) {
      long long int dpc[505][505];
      for (long long int j = 0; j <= 500; j++) {
        for (long long int k = 0; k <= m; k++) {
          dpc[j][k] = inf;
        }
      }
      long long int c = a[i] - '0';
      for (long long int j = 0; j <= 500; j++) {
        for (long long int k = 0; k <= m; k++) {
          if (dp[j][k] == inf) {
            continue;
          }
          if (aut[k][c] == m) {
            dpc[j + 1][aut[k][c]] = min(dpc[j + 1][aut[k][c]], dp[j][k]);
          } else {
            dpc[j][aut[k][c]] = min(dpc[j][aut[k][c]], dp[j][k]);
          }
          if (aut[k][c ^ 1] == m) {
            dpc[j + 1][aut[k][c ^ 1]] =
                min(dpc[j + 1][aut[k][c ^ 1]], dp[j][k] + 1);
          } else {
            dpc[j][aut[k][c ^ 1]] = min(dpc[j][aut[k][c ^ 1]], dp[j][k] + 1);
          }
        }
      }
      for (long long int j = 0; j <= 500; j++) {
        for (long long int k = 0; k <= m; k++) {
          dp[j][k] = dpc[j][k];
        }
      }
    }
    for (long long int i = 0; i <= n - m + 1; i++) {
      long long int v = inf;
      for (long long int j = 0; j <= m; j++) {
        v = min(v, dp[i][j]);
      }
      if (v < inf) {
        cout << v << " ";
      } else {
        cout << "-1 ";
      }
    }
  }
  