#include <bits/stdc++.h>
using namespace std;
const int S = 30;
const int N = 2e5 + 10;
const long long MOD = 2038074713LL;
const long long BASE_MODULAR_INVERSE = 1019037357;
const int HASH_INT_SIZE = 20;
int nt, ns;
string s, t;
set<long long> t_hashes, seg_hashes;
unordered_map<long long, int> t_hash_to_char;
long long _char_hash_in_t[S];
long long pos_t[N], neg_t[N];
long long _hash_array[S];
set<int> _ind[S];
char _match[S];
bool _mark[S], old_hash[S];
vector<char> sigma;
int system_time;
void build_hash_t();
void build_first_hash_s();
bool check();
bool make_match(char);
void move_right(int, int);
void pre_proc();
void add(char, int);
void del(char, int);
set<int> &ind(char);
char &match(char);
bool &mark(char);
long long &char_hash_in_t(char);
long long &hash_array(char);
void cerr_hash(string, bool = true);
int32_t main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  for (char c = 'a'; c <= 'z'; c++) sigma.push_back(c);
  cin >> ns >> nt;
  cin >> s >> t;
  pre_proc();
  t_hash_to_char.reserve(1 << 5);
  t_hash_to_char.max_load_factor(0.25);
  build_hash_t();
  cerr_hash("T:");
  build_first_hash_s();
  cerr_hash("first S:");
  int l = 0, r = nt;
  vector<int> ans;
  while (r <= ns) {
    cerr_hash("\n\nsegment [" + to_string(l) + ',' + to_string(r) + "): ");
    if (check()) {
      ans.push_back(l);
    }
    if (r < ns) move_right(l, r);
    l++;
    r++;
  }
  cout << ans.size() << endl;
  for (int i : ans) cout << i + 1 << ' ';
  cout << endl;
}
void pre_proc() {
  pos_t[0] = 1;
  neg_t[0] = MOD - 1;
  for (int i = 1; i <= ns + 2; i++) {
    pos_t[i] = (pos_t[i - 1] * 2) % MOD;
    neg_t[i] = (pos_t[i - 1] * 2) % MOD;
  }
}
void build_hash_t() {
  for (int i = 0; i < nt; i++) {
    ind(t[i]).insert(i);
    add(t[i], i);
  }
  for (char c : sigma) {
    long long cur_hash = hash_array(c);
    char_hash_in_t(c) = cur_hash;
    assert(ind(c).empty() || t_hashes.find(cur_hash) == t_hashes.end());
    t_hashes.insert(cur_hash);
    if (!ind(c).empty()) t_hash_to_char[cur_hash] = c;
  }
}
void build_first_hash_s() {
  for (char c : sigma) {
    ind(c).clear();
    hash_array(c) = 0;
  }
  for (int i = 0; i < nt; i++) {
    ind(s[i]).insert(i);
    add(s[i], i);
  }
}
bool check() {
  for (char c : sigma) mark(c) = false;
  seg_hashes.clear();
  for (char c : sigma) seg_hashes.insert(hash_array(c));
  if (seg_hashes != t_hashes) return false;
  for (char c : sigma)
    if (!mark(c) && !ind(c).empty())
      if (!make_match(c)) {
        return false;
      }
  return true;
}
bool make_match(char c) {
  match(c) = t_hash_to_char[hash_array(c)];
  if (mark(match(c))) return false;
  mark(match(c)) = true;
  if (hash_array(match(c)) != char_hash_in_t(c)) return false;
  match(match(c)) = c;
  return true;
}
void move_right(int l, int r) {
  cerr_hash("before move " + to_string(l) + ": ", false);
  ind(s[l]).erase(l);
  ind(s[r]).insert(r);
  del(s[l], 0);
  add(s[r], nt);
  cerr_hash("before move1 " + to_string(l) + ": ", false);
  for (char c : sigma)
    hash_array(c) = (hash_array(c) * BASE_MODULAR_INVERSE) % MOD;
  cerr_hash("after move2 " + to_string(l) + ": ", false);
  system_time++;
}
void add(char c, int val) {
  hash_array(c) = (hash_array(c) + pos_t[val]) % MOD;
}
void del(char c, int val) {
  hash_array(c) = (hash_array(c) + neg_t[val]) % MOD;
}
void cerr_hash(string msg, bool tt) {
  tt = true;
  if (tt) return;
  cout << msg << endl;
  for (char c : sigma) {
    if (ind(c).size() == 0) continue;
    cout << c << ": ";
    for (int i : ind(c)) cout << i << "(=" << i - system_time << ") ";
    cout << " -> " << hash_array(c) << endl;
  }
}
long long &hash_array(char c) { return _hash_array[int(c - 'a')]; }
set<int> &ind(char c) { return _ind[int(c - 'a')]; }
char &match(char c) { return _match[int(c - 'a')]; }
bool &mark(char c) { return _mark[int(c - 'a')]; }
long long &char_hash_in_t(char c) { return _char_hash_in_t[int(c - 'a')]; }

### Prompt

Your task is to create a Cpp solution to the following problem:

Polycarp invented a new way to encode strings. Let's assume that we have string T, consisting of lowercase English letters. Let's choose several pairs of letters of the English alphabet in such a way that each letter occurs in at most one pair. Then let's replace each letter in T with its pair letter if there is a pair letter for it. For example, if you chose pairs (l, r), (p, q) and (a, o), then word "parallelogram" according to the given encoding principle transforms to word "qolorreraglom".

Polycarpus already has two strings, S and T. He suspects that string T was obtained after applying the given encoding method from some substring of string S. Find all positions mi in S (1 ≤ mi ≤ |S| - |T| + 1), such that T can be obtained fro substring SmiSmi + 1... Smi + |T| - 1 by applying the described encoding operation by using some set of pairs of English alphabet letters

Input

The first line of the input contains two integers, |S| and |T| (1 ≤ |T| ≤ |S| ≤ 2·105) — the lengths of string S and string T, respectively.

The second and third line of the input contain strings S and T, respectively. Both strings consist only of lowercase English letters.

Output

Print number k — the number of suitable positions in string S.

In the next line print k integers m1, m2, ..., mk — the numbers of the suitable positions in the increasing order.

Examples

Input

11 5
abacabadaba
acaba


Output

3
1 3 7


Input

21 13
paraparallelogramgram
qolorreraglom


Output

1
5

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int S = 30;
const int N = 2e5 + 10;
const long long MOD = 2038074713LL;
const long long BASE_MODULAR_INVERSE = 1019037357;
const int HASH_INT_SIZE = 20;
int nt, ns;
string s, t;
set<long long> t_hashes, seg_hashes;
unordered_map<long long, int> t_hash_to_char;
long long _char_hash_in_t[S];
long long pos_t[N], neg_t[N];
long long _hash_array[S];
set<int> _ind[S];
char _match[S];
bool _mark[S], old_hash[S];
vector<char> sigma;
int system_time;
void build_hash_t();
void build_first_hash_s();
bool check();
bool make_match(char);
void move_right(int, int);
void pre_proc();
void add(char, int);
void del(char, int);
set<int> &ind(char);
char &match(char);
bool &mark(char);
long long &char_hash_in_t(char);
long long &hash_array(char);
void cerr_hash(string, bool = true);
int32_t main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  for (char c = 'a'; c <= 'z'; c++) sigma.push_back(c);
  cin >> ns >> nt;
  cin >> s >> t;
  pre_proc();
  t_hash_to_char.reserve(1 << 5);
  t_hash_to_char.max_load_factor(0.25);
  build_hash_t();
  cerr_hash("T:");
  build_first_hash_s();
  cerr_hash("first S:");
  int l = 0, r = nt;
  vector<int> ans;
  while (r <= ns) {
    cerr_hash("\n\nsegment [" + to_string(l) + ',' + to_string(r) + "): ");
    if (check()) {
      ans.push_back(l);
    }
    if (r < ns) move_right(l, r);
    l++;
    r++;
  }
  cout << ans.size() << endl;
  for (int i : ans) cout << i + 1 << ' ';
  cout << endl;
}
void pre_proc() {
  pos_t[0] = 1;
  neg_t[0] = MOD - 1;
  for (int i = 1; i <= ns + 2; i++) {
    pos_t[i] = (pos_t[i - 1] * 2) % MOD;
    neg_t[i] = (pos_t[i - 1] * 2) % MOD;
  }
}
void build_hash_t() {
  for (int i = 0; i < nt; i++) {
    ind(t[i]).insert(i);
    add(t[i], i);
  }
  for (char c : sigma) {
    long long cur_hash = hash_array(c);
    char_hash_in_t(c) = cur_hash;
    assert(ind(c).empty() || t_hashes.find(cur_hash) == t_hashes.end());
    t_hashes.insert(cur_hash);
    if (!ind(c).empty()) t_hash_to_char[cur_hash] = c;
  }
}
void build_first_hash_s() {
  for (char c : sigma) {
    ind(c).clear();
    hash_array(c) = 0;
  }
  for (int i = 0; i < nt; i++) {
    ind(s[i]).insert(i);
    add(s[i], i);
  }
}
bool check() {
  for (char c : sigma) mark(c) = false;
  seg_hashes.clear();
  for (char c : sigma) seg_hashes.insert(hash_array(c));
  if (seg_hashes != t_hashes) return false;
  for (char c : sigma)
    if (!mark(c) && !ind(c).empty())
      if (!make_match(c)) {
        return false;
      }
  return true;
}
bool make_match(char c) {
  match(c) = t_hash_to_char[hash_array(c)];
  if (mark(match(c))) return false;
  mark(match(c)) = true;
  if (hash_array(match(c)) != char_hash_in_t(c)) return false;
  match(match(c)) = c;
  return true;
}
void move_right(int l, int r) {
  cerr_hash("before move " + to_string(l) + ": ", false);
  ind(s[l]).erase(l);
  ind(s[r]).insert(r);
  del(s[l], 0);
  add(s[r], nt);
  cerr_hash("before move1 " + to_string(l) + ": ", false);
  for (char c : sigma)
    hash_array(c) = (hash_array(c) * BASE_MODULAR_INVERSE) % MOD;
  cerr_hash("after move2 " + to_string(l) + ": ", false);
  system_time++;
}
void add(char c, int val) {
  hash_array(c) = (hash_array(c) + pos_t[val]) % MOD;
}
void del(char c, int val) {
  hash_array(c) = (hash_array(c) + neg_t[val]) % MOD;
}
void cerr_hash(string msg, bool tt) {
  tt = true;
  if (tt) return;
  cout << msg << endl;
  for (char c : sigma) {
    if (ind(c).size() == 0) continue;
    cout << c << ": ";
    for (int i : ind(c)) cout << i << "(=" << i - system_time << ") ";
    cout << " -> " << hash_array(c) << endl;
  }
}
long long &hash_array(char c) { return _hash_array[int(c - 'a')]; }
set<int> &ind(char c) { return _ind[int(c - 'a')]; }
char &match(char c) { return _match[int(c - 'a')]; }
bool &mark(char c) { return _mark[int(c - 'a')]; }
long long &char_hash_in_t(char c) { return _char_hash_in_t[int(c - 'a')]; }

```