This is a simplified version of the task Toy Train. These two versions differ only in the constraints. Hacks for this version are disabled.

Alice received a set of Toy Train™ from Bob. It consists of one train and a connected railway network of n stations, enumerated from 1 through n. The train occupies one station at a time and travels around the network of stations in a circular manner. More precisely, the immediate station that the train will visit after station i is station i+1 if 1 ≤ i < n or station 1 if i = n. It takes the train 1 second to travel to its next station as described.

Bob gave Alice a fun task before he left: to deliver m candies that are initially at some stations to their independent destinations using the train. The candies are enumerated from 1 through m. Candy i (1 ≤ i ≤ m), now at station a_i, should be delivered to station b_i (a_i ≠ b_i).

<image> The blue numbers on the candies correspond to b_i values. The image corresponds to the 1-st example.

The train has infinite capacity, and it is possible to load off any number of candies at a station. However, only at most one candy can be loaded from a station onto the train before it leaves the station. You can choose any candy at this station. The time it takes to move the candies is negligible.

Now, Alice wonders how much time is needed for the train to deliver all candies. Your task is to find, for each station, the minimum time the train would need to deliver all the candies were it to start from there.

Input

The first line contains two space-separated integers n and m (2 ≤ n ≤ 100; 1 ≤ m ≤ 200) — the number of stations and the number of candies, respectively.

The i-th of the following m lines contains two space-separated integers a_i and b_i (1 ≤ a_i, b_i ≤ n; a_i ≠ b_i) — the station that initially contains candy i and the destination station of the candy, respectively.

Output

In the first and only line, print n space-separated integers, the i-th of which is the minimum time, in seconds, the train would need to deliver all the candies were it to start from station i.

Examples

Input


5 7
2 4
5 1
2 3
3 4
4 1
5 3
3 5


Output


10 9 10 10 9 


Input


2 3
1 2
1 2
1 2


Output


5 6 

Note

Consider the second sample.

If the train started at station 1, the optimal strategy is as follows.

  1. Load the first candy onto the train. 
  2. Proceed to station 2. This step takes 1 second. 
  3. Deliver the first candy. 
  4. Proceed to station 1. This step takes 1 second. 
  5. Load the second candy onto the train. 
  6. Proceed to station 2. This step takes 1 second. 
  7. Deliver the second candy. 
  8. Proceed to station 1. This step takes 1 second. 
  9. Load the third candy onto the train. 
  10. Proceed to station 2. This step takes 1 second. 
  11. Deliver the third candy. 



Hence, the train needs 5 seconds to complete the tasks.

If the train were to start at station 2, however, it would need to move to station 1 before it could load the first candy, which would take one additional second. Thus, the answer in this scenario is 5+1 = 6 seconds.
#include <bits/stdc++.h>
using namespace std;
char string_in_buffer[(int)260];
void fast_scan(int &first) { scanf("%d", &first); }
void fast_scan(long long &first) { scanf("%lld", &first); }
void fast_scan(unsigned long long &first) { scanf("%llu", &first); }
void fast_scan(double &first) { scanf("%lf", &first); }
void fast_scan(long double &first) { scanf("%Lf", &first); }
void fast_scan(char &first) {
  scanf("%c", &first);
  if (first == '\n') {
    fast_scan(first);
  }
}
void fast_scan(string &first) {
  scanf("%s", string_in_buffer);
  first = string(string_in_buffer);
}
template <class TFirst, class TSecond>
void fast_scan(pair<TFirst, TSecond> &p) {
  fast_scan(p.first);
  fast_scan(p.second);
}
template <class T>
void fast_scan(vector<T> &v) {
  for (auto &first : v) fast_scan(first);
}
void fast_print(const int &first) { printf("%d", first); }
void fast_print(const unsigned int &first) { printf("%u", first); }
void fast_print(const long long &first) { printf("%lld", first); }
void fast_print(const unsigned long long &first) { printf("%llu", first); }
void fast_print(const double &first) { printf("%.15lf", first); }
void fast_print(const long double &first) { printf("%.15Lf", first); }
void fast_print(const char &first) { printf("%c", first); };
void fast_print(const string &first) { printf("%s", first.c_str()); }
void fast_print(const char v[]) { fast_print((string)v); }
template <class TFirst, class TSecond>
void fast_print(const pair<TFirst, TSecond> &p) {
  fast_print(p.first);
  fast_print(' ');
  fast_print(p.second);
}
template <class T>
void fast_print(const vector<T> &v) {
  if (v.empty()) return;
  fast_print(v[0]);
  for (int i = 1; i < v.size(); i++) {
    fast_print(' ');
    fast_print(v[i]);
  }
}
template <class T>
void fast_print(const vector<vector<T>> &v) {
  if (v.empty()) return;
  fast_print(v[0]);
  for (int i = 1; i < v.size(); i++) {
    fast_print('\n');
    fast_print(v[i]);
  }
}
template <class T>
void fast_print(const T &v) {
  for (const auto &first : v) {
    fast_print(first);
    fast_print(' ');
  }
}
using namespace std;
namespace smart_io {
string print_start = "";
string sep = " ";
bool first_print = false;
void precall_print() {
  fast_print(print_start);
  print_start = "\n";
  first_print = true;
}
void _print(deque<string>) {}
template <class T, class... Args>
void _print(deque<string> names, T elem, Args... args) {
  if (!first_print) {
    fast_print("\n");
  } else {
    first_print = false;
  }
  fast_print(names.front());
  fast_print(" = ");
  fast_print(elem);
  names.pop_front();
  _print(names, args...);
}
}  // namespace smart_io
template <class T>
ostream &operator,(ostream &os, const T &object) {
  if (!smart_io::first_print) {
    fast_print(smart_io::sep);
  } else {
    smart_io::first_print = false;
  }
  fast_print(object);
  return os;
}
template <class T>
istream &operator,(istream &is, T &object) {
  fast_scan(object);
  return is;
}
namespace escape__from__random__aetuhoetnuhshe {
using namespace std::chrono;
mt19937 rng(duration_cast<milliseconds>(system_clock::now().time_since_epoch())
                .count());
uniform_real_distribution<> prob_dist(0.0, 1.0);
};  // namespace escape__from__random__aetuhoetnuhshe
namespace typedefs {}
namespace numbers_operation {
template <class T>
T floor_mod(T a, T b) {
  if (a >= 0 && b >= 0) return a % b;
  if (a <= 0 && b <= 0) return a % b;
  return abs(b) - (abs(a) % abs(b));
}
}  // namespace numbers_operation
using namespace numbers_operation;
using namespace typedefs;
using namespace escape__from__random__aetuhoetnuhshe;
long long n, m;
vector<vector<long long>> g;
signed main(signed argc, char *argv[]) {
  cin, n, m;
  g.resize(n);
  for (long long i = 0; i < (m); i++) {
    long long a, b;
    cin, a, b;
    a--;
    b--;
    g[a].push_back(b);
  }
  vector<long long> time;
  for (long long i = 0; i < n; i++) {
    if (g[i].empty()) {
      time.push_back(-2 * n);
      continue;
    }
    time.push_back(((long long)g[i].size()) * n - n);
    long long _min = 1e9;
    for (long long sub : g[i]) {
      _min = min(_min, floor_mod(sub - i, n));
    }
    time.back() += _min;
  }
  multiset<long long> L, R;
  long long ML = 0, MR = 0;
  for (long long i = 0; i < (n); i++) {
    R.insert(time[i] + i);
  }
  for (long long i = 0; i < (n); i++) {
    long long result = max((L.empty() ? -1e9 : *L.rbegin()) + ML,
                           (R.empty() ? -1e9 : *R.rbegin()) + MR);
    smart_io::precall_print();
    cout, result;
    smart_io::print_start = " ";
    R.erase(R.find(time[i] + i));
    ML--;
    MR--;
    L.insert(time[i] - ML + n - 1);
  }
}
