Problem: You are given two strings s and t consisting of lowercase Latin letters. The length of t is 2 (i.e. this string consists only of two characters).

In one move, you can choose any character of s and replace it with any lowercase Latin letter. More formally, you choose some i and replace s_i (the character at the position i) with some character from 'a' to 'z'.

You want to do no more than k replacements in such a way that maximizes the number of occurrences of t in s as a subsequence.

Recall that a subsequence is a sequence that can be derived from the given sequence by deleting zero or more elements without changing the order of the remaining elements.

Input

The first line of the input contains two integers n and k (2 ≤ n ≤ 200; 0 ≤ k ≤ n) — the length of s and the maximum number of moves you can make. The second line of the input contains the string s consisting of n lowercase Latin letters. The third line of the input contains the string t consisting of two lowercase Latin letters.

Output

Print one integer — the maximum possible number of occurrences of t in s as a subsequence if you replace no more than k characters in s optimally.

Examples

Input


4 2
bbaa
ab


Output


3


Input


7 3
asddsaf
sd


Output


10


Input


15 6
qwertyhgfdsazxc
qa


Output


16


Input


7 2
abacaba
aa


Output


15

Note

In the first example, you can obtain the string "abab" replacing s_1 with 'a' and s_4 with 'b'. Then the answer is 3.

In the second example, you can obtain the string "ssddsdd" and get the answer 10.

In the fourth example, you can obtain the string "aaacaaa" and get the answer 15.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <typename A, typename B>
string to_string(pair<A, B> p);
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);
string to_string(const string &s) { return '"' + s + '"'; }
string to_string(const char *s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "true" : "false"); }
string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}
template <size_t N>
string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}
template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ")";
}
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + "," +
         to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}
void debug() { cerr << endl; }
template <typename Head, typename... Tail>
void debug(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug(T...);
}
struct Fast_power {
  long long integer(long long n, long long e,
                    long long my_mod = 9223372036854775807LL) {
    long long ans = 1;
    while (e) {
      if (e & 1)
        ans = (ans * n) % my_mod, e--;
      else
        n = (n * n) % my_mod, e >>= 1;
    }
    return ans;
  }
  vector<vector<long long>> matrix_multiply(vector<vector<long long>> a,
                                            vector<vector<long long>> b) {
    vector<vector<long long>> c(a.size(), vector<long long>(b[0].size(), 0));
    for (int i = 0; i < a.size(); i++)
      for (int q = 0; q < b[0].size(); q++) {
        long long num = 0;
        for (int e = 0; e < a[0].size(); i++) num += a[i][e] * b[e][q];
        c[i][q] = num;
      }
    return c;
  }
};
struct Euclidean {
  int gcdi(int a, int b) { return b ? gcdi(b, a % b) : a; }
  double gcdf(double a, double b, double accuracy) {
    return b <= accuracy ? a : gcdf(b, fmod(a, b), accuracy);
  }
};
const int maxnD = 100000 + 5;
const long long INFD = 0x3f3f3f3f;
;
struct Dijkstra {
  struct Edge {
    int from, to;
    long long dist;
  };
  struct HeapNode {
    long long d;
    int u;
    bool operator<(const HeapNode &rhs) const { return d > rhs.d; }
  };
  vector<Edge> edges;
  vector<int> G[maxnD];
  bool done[maxnD];
  long long d[maxnD];
  int p[maxnD], n;
  void init(int n) {
    this->n = n;
    for (int i = 0; i <= n; i++) G[i].clear();
    edges.clear();
  }
  void AddEdge(int from, int to, long long dist) {
    edges.push_back((Edge){from, to, dist});
    int m = edges.size();
    G[from].push_back(m - 1);
  }
  void dijkstra(int s) {
    priority_queue<HeapNode> q;
    memset(d, INFD, sizeof(d));
    d[s] = 0;
    memset(done, 0, sizeof(done));
    q.push((HeapNode){0, s});
    while (!q.empty()) {
      HeapNode x = q.top();
      q.pop();
      int u = x.u;
      if (done[u]) continue;
      done[u] = true;
      for (int i = 0; i < G[u].size(); i++) {
        Edge &e = edges[G[u][i]];
        if (d[e.to] > d[u] + e.dist) {
          d[e.to] = d[u] + e.dist;
          p[e.to] = G[u][i];
          q.push((HeapNode){d[e.to], e.to});
        }
      }
    }
  }
};
const int maxnL = 500000 + 5;
const int INFL = 0x3f3f3f3f;
struct LIS {
  int g[maxnL], a[maxnL], d[maxnL];
  void lis(int n) {
    for (int i = 1; i <= n; i++) g[i] = INFL;
    for (int i = 1; i < n; i++) {
      int k = lower_bound(g + 1, g + n + 1, a[i]) - g;
      g[k] = a[i];
    }
  }
};
const int maxnS = 200000 + 5;
struct SegmentTree {
  int a[maxnS];
  int sumv[maxnS * 4], minv[maxnS * 4], maxv[maxnS * 4], addv[maxnS * 4],
      setv[maxnS * 4];
  int lc, rc, v;
  int _min, _max, _sum;
  void build(int l, int r, int o) {
    if (l == r) return void(sumv[o] = minv[o] = maxv[o] = a[l]);
    build(l, (l + r) >> 1, o << 1);
    build(((l + r) >> 1) + 1, r, o << 1 | 1);
  }
  void maintain(int l, int r, int o) {
    sumv[o] = minv[o] = maxv[o] = a[l];
    if (r > l) {
      sumv[o] = sumv[o << 1] + sumv[o << 1 | 1];
      minv[o] = min(minv[o << 1], minv[o << 1 | 1]);
      maxv[o] = max(maxv[o << 1], maxv[o << 1 | 1]);
    }
    minv[o] += addv[o], maxv[o] += addv[o], sumv[o] += addv[o] * (r - l + 1);
  }
  void update(int l, int r, int o) {
    if (l >= lc && r <= rc)
      addv[o] += v;
    else {
      int m = (l + r) >> 1;
      if (lc <= m) update(l, (l + r) >> 1, o << 1);
      if (rc > m) update(((l + r) >> 1) + 1, r, o << 1 | 1);
    }
    maintain(l, r, o);
  }
  void query(int l, int r, int o, int add) {
    if (lc <= l && r <= rc) {
      _sum += sumv[o] + add * (r - l + 1);
      _min = min(_min, minv[o] + add);
      _max = max(_max, maxv[o] + add);
    } else {
      int m = (l + r) >> 1;
      if (lc <= m) query(l, m, o << 1, add + addv[o]);
      if (rc > m) query(m + 1, r, o << 1 | 1, add + addv[o]);
    }
  }
};
const int maxnB = 100000 + 5;
struct BIT {
  int c[maxnB], n;
  int lowbit(int x) { return x & -x; }
  int sum(int x) {
    int ret = 0;
    while (x > 0) {
      ret += c[x];
      x -= lowbit(x);
    }
    return ret;
  }
  void add(int x, int d) {
    while (x <= n) {
      c[x] += d;
      x += lowbit(x);
    }
  }
};
const int INF = 0x3f3f3f3f;
const int maxn = 200 + 5;
int d[maxn][maxn][maxn], f[maxn][maxn][maxn];
char str[maxn], s[maxn];
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, k;
  cin >> n >> k;
  memset(d, -1, sizeof(d));
  d[0][0][0] = 0;
  cin >> str + 1 >> s;
  for (int i = 1; i <= n; i++)
    for (int q = 0; q <= k; q++)
      for (int e = 0; e <= n; e++) {
        if (d[i - 1][q][e] != -1) d[i][q][e] = d[i - 1][q][e];
        if (str[i] == s[1])
          if (d[i - 1][q][e] != -1)
            d[i][q][e] = max(d[i][q][e], d[i - 1][q][e] + e);
        if (e > 0 && str[i] == s[0])
          if (d[i - 1][q][e - 1] != -1)
            d[i][q][e] = max(d[i - 1][q][e - 1], d[i][q][e]);
        if (q > 0) {
          if (d[i - 1][q - 1][e] != -1)
            d[i][q][e] = max(d[i][q][e], d[i - 1][q - 1][e] + e);
          if (e > 0 && d[i - 1][q - 1][e - 1] != -1)
            d[i][q][e] = max(d[i - 1][q - 1][e - 1], d[i][q][e]);
        }
      }
  int ans = 0;
  for (int i = 1; i <= n; i++)
    for (int q = 0; q <= k; q++)
      for (int e = 0; e <= n; e++) ans = max(d[i][q][e], ans);
  if (s[0] == s[1]) {
    int num = 0;
    for (int i = 1; i <= n; i++)
      if (str[i] == s[0]) num++;
    int num2 = num + min(k, n - num);
    ans = num2 * (num2 - 1) / 2;
  }
  cout << ans << endl;
  return 0;
}