#include <bits/stdc++.h>

#define M_PI 3.14159265358979323846

using namespace std;

//typedef
//-------------------------#include <bits/stdc++.h>

#define M_PI 3.14159265358979323846

using namespace std;

//conversion
//------------------------------------------
inline int toInt(string s)
{
  int v;
  istringstream sin(s);
  sin >> v;
  return v;
}
template <class T>
inline string toString(T x)
{
  ostringstream sout;
  sout << x;
  return sout.str();
}
inline int readInt()
{
  int x;
  scanf("%d", &x);
  return x;
}

//typedef
//------------------------------------------
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<string> VS;
typedef pair<int, int> PII;
typedef pair<int, PII> TIII;
typedef long long LL;
typedef unsigned long long ULL;
typedef vector<LL> VLL;
typedef vector<VLL> VVLL;

//container util

//------------------------------------------
#define ALL(a) (a).begin(), (a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define PB push_back
#define MP make_pair
#define SZ(a) int((a).size())
#define SQ(a) ((a) * (a))
#define EACH(i, c) for (typeof((c).begin()) i = (c).begin(); i != (c).end(); ++i)
#define EXIST(s, e) ((s).find(e) != (s).end())
#define SORT(c) sort((c).begin(), (c).end())

//repetition
//------------------------------------------
#define FOR(i, s, n) for (int i = s; i < (int)n; ++i)
#define REP(i, n) FOR(i, 0, n)
#define MOD 1000000007

#define rep(i, a, b) for (int i = a; i < (b); ++i)
#define trav(a, x) for (auto &a : x)
#define all(x) x.begin(), x.end()
#define sz(x) (int)(x).size()

typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
const double EPS = 1E-8;

#define chmin(x, y) x = min(x, y)
#define chmax(x, y) x = max(x, y)
const int INF = 100000000;

struct Edge
{
  int to, from;
  ll cost;
  Edge(int from, int to, ll cost) : from(from), to(to), cost(cost) {}
};

class UnionFind
{
public:
  vector<ll> par;
  vector<ll> siz;

  vector<ll> maxv;
  UnionFind(ll sz_) : par(sz_), siz(sz_, 1LL)
  {
    for (ll i = 0; i < sz_; ++i)
      par[i] = i;
  }
  void init(ll sz_)
  {
    par.resize(sz_);
    siz.assign(sz_, 1LL);
    for (ll i = 0; i < sz_; ++i)
      par[i] = i;
  }

  ll root(ll x)
  {
    while (par[x] != x)
    {
      x = par[x] = par[par[x]];
    }
    return x;
  }

  bool merge(ll x, ll y)
  {
    x = root(x);
    y = root(y);
    if (x == y)
      return false;
    if (siz[x] < siz[y])
      swap(x, y);
    siz[x] += siz[y];
    par[y] = x;
    return true;
  }

  bool issame(ll x, ll y)
  {
    return root(x) == root(y);
  }

  ll size(ll x)
  {
    return siz[root(x)];
  }
};

typedef vector<vector<Edge>> AdjList;
AdjList graph;

ll mod_pow(ll x, ll n, ll mod)
{
  ll res = 1;
  bool c = false;
  while (n)
  {
    if (n & 1)
      res = res * x;

    if (res > mod)
    {
      c = true;
      res %= mod;
    }
    x = x * x % mod;
    n >>= 1;
  }
  if (c)
    return mod;
  return res;
}

#define SIEVE_SIZE 5000000 + 10
bool sieve[SIEVE_SIZE];
void make_sieve()
{
  for (int i = 0; i < SIEVE_SIZE; ++i)
    sieve[i] = true;
  sieve[0] = sieve[1] = false;
  for (int i = 2; i * i < SIEVE_SIZE; ++i)
    if (sieve[i])
      for (int j = 2; i * j < SIEVE_SIZE; ++j)
        sieve[i * j] = false;
}

bool isprime(ll n)
{
  if (n == 0 || n == 1)
    return false;
  for (ll i = 2; i * i <= n; ++i)
    if (n % i == 0)
      return false;
  return true;
}

template <typename T>
vector<T> gauss_jordan(const vector<vector<T>> &A, const vector<T> &b)
{
  int n = A.size();
  vector<vector<T>> B(n, vector<T>(n + 1));

  for (int i = 0; i < n; ++i)
  {
    for (int j = 0; j < n; ++j)
    {
      B[i][j] = A[i][j];
    }
  }

  for (int i = 0; i < n; ++i)
    B[i][n] = b[i];

  for (int i = 0; i < n; ++i)
  {
    int pivot = i;
    for (int j = i; j < n; ++j)
    {
      if (abs(B[j][i]) > abs(B[pivot][i]))
        pivot = j;
    }
    swap(B[i], B[pivot]);

    if (abs(B[i][i]) < EPS)
      return vector<T>(); //解なし

    for (int j = i + 1; j <= n; ++j)
      B[i][j] /= B[i][i];
    for (int j = 0; j < n; ++j)
    {
      if (i != j)
      {
        for (int k = i + 1; k <= n; ++k)
          B[j][k] -= B[i][j] * B[i][k];
      }
    }
  }

  vector<T> x(n);

  for (int i = 0; i < n; ++i)
    x[i] = B[i][n];
  return x;
}

typedef vector<ll> vec;
typedef vector<vec> mat;

mat mul(mat &A, mat &B)
{
  mat C(A.size(), vec((int)B[0].size()));
  for (int i = 0; i < A.size(); ++i)
  {
    for (int k = 0; k < B.size(); ++k)
    {
      for (int j = 0; j < B[0].size(); ++j)
      {
        C[i][j] = (C[i][j] + A[i][k] * B[k][j] % MOD) % MOD;
      }
    }
  }
  return C;
}
mat mat_pow(mat A, ll n)
{
  mat B(A.size(), vec((int)A.size()));

  for (int i = 0; i < A.size(); ++i)
  {
    B[i][i] = 1;
  }

  while (n > 0)
  {
    if (n & 1)
      B = mul(B, A);
    A = mul(A, A);
    n >>= 1;
  }
  return B;
}

bool operator<(const pii &a, const pii &b)
{
  if (a.first == b.first)
    return a.second < b.second;
  return a.first < b.first;
}

const int MAX = 510000;
long long fac[MAX], finv[MAX], inv[MAX];

// テーブルを作る前処理
void COMinit()
{
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  for (int i = 2; i < MAX; i++)
  {
    fac[i] = fac[i - 1] * i % MOD;
    inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
    finv[i] = finv[i - 1] * inv[i] % MOD;
  }
}

// 二項係数計算
long long COM(int n, int k)
{
  if (n < k)
    return 0;
  if (n < 0 || k < 0)
    return 0;
  return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}

int bit[1000010];
int sums(int i)
{
  i++;
  int s = 0;
  while (i > 0)
  {
    s += bit[i];
    i -= i & -i;
  }
  return s;
}
void add(int i, int x)
{
  i++;
  while (i <= 1000010)
  {
    bit[i] += x;
    i += i & -i;
  }
}
long long extGCD(long long a, long long b, long long &x, long long &y)
{
  if (b == 0)
  {
    x = 1;
    y = 0;
    return a;
  }
  long long d = extGCD(b, a % b, y, x);
  y -= a / b * x;
  return d;
}

ll GCD(ll a, ll b)
{

  if (b == 0)
    return a;
  return GCD(b, a % b);
}

struct BipartiteMatching
{
  vector<vector<int>> graph;
  vector<int> match, alive, used;
  int timestamp;

  BipartiteMatching(int n) : graph(n), alive(n, 1), used(n, 0), match(n, -1), timestamp(0) {}

  void add_edge(int u, int v)
  {
    graph[u].push_back(v);
    graph[v].push_back(u);
  }

  bool dfs(int idx)
  {
    used[idx] = timestamp;
    for (auto &to : graph[idx])
    {
      int to_match = match[to];
      if (alive[to] == 0)
        continue;
      if (to_match == -1 || (used[to_match] != timestamp && dfs(to_match)))
      {
        match[idx] = to;
        match[to] = idx;
        return true;
      }
    }
    return false;
  }

  int bipartite_matching()
  {
    int ret = 0;
    for (int i = 0; i < graph.size(); i++)
    {
      if (alive[i] == 0)
        continue;
      if (match[i] == -1)
      {
        ++timestamp;
        ret += dfs(i);
      }
    }
    return ret;
  }

  void output()
  {
    for (int i = 0; i < graph.size(); i++)
    {
      if (i < match[i])
      {
        cout << i << "-" << match[i] << endl;
      }
    }
  }
};

int dp[200010];

bool used[200010];
int stock[200010];
int main()
{
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(15);

  int n, m;
  cin >> n >> m;

  vector<pair<int, int>> vp;
  for (int i = 0; i < m; i++)
  {
    int x, y;
    cin >> x >> y;
    vp.push_back({x, y});
  }
  for (int i = 1; i <= n; i++)
    dp[i] = 1;

  sort(all(vp));

  map<int, pair<int, int>> mp;
  for (int i = 0; i < vp.size(); i++)
  {
    int x = vp[i].first, y = vp[i].second;

    if (!used[y])
    {
      int t1 = dp[y], t2 = dp[y + 1];
      dp[y] += t2;
      dp[y + 1] += t1;
      mp[y] = make_pair(dp[y], dp[y + 1]);
      used[y] = true;
    }
    else
    {
      int sa1 = dp[y] - mp[y].first;
      int sa2 = dp[y + 1] - mp[y].second;

      dp[y + 1] += sa1;
      dp[y] += sa2;
      mp[y] = make_pair(dp[y], dp[y + 1]);
    }
  }
  for (int i = 1; i <= n; i++)
  {
    if (i - 1)
      cout << " ";

    cout << dp[i];
  }
  cout << endl;
  return 0;
}


### Prompt

Please create a solution in CPP to the following problem:

Example

Input

4 3
1000 1
2000 2
3000 3


Output

2 3 4 4

### Response

```cpp
#include <bits/stdc++.h>

#define M_PI 3.14159265358979323846

using namespace std;

//typedef
//-------------------------#include <bits/stdc++.h>

#define M_PI 3.14159265358979323846

using namespace std;

//conversion
//------------------------------------------
inline int toInt(string s)
{
  int v;
  istringstream sin(s);
  sin >> v;
  return v;
}
template <class T>
inline string toString(T x)
{
  ostringstream sout;
  sout << x;
  return sout.str();
}
inline int readInt()
{
  int x;
  scanf("%d", &x);
  return x;
}

//typedef
//------------------------------------------
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<string> VS;
typedef pair<int, int> PII;
typedef pair<int, PII> TIII;
typedef long long LL;
typedef unsigned long long ULL;
typedef vector<LL> VLL;
typedef vector<VLL> VVLL;

//container util

//------------------------------------------
#define ALL(a) (a).begin(), (a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define PB push_back
#define MP make_pair
#define SZ(a) int((a).size())
#define SQ(a) ((a) * (a))
#define EACH(i, c) for (typeof((c).begin()) i = (c).begin(); i != (c).end(); ++i)
#define EXIST(s, e) ((s).find(e) != (s).end())
#define SORT(c) sort((c).begin(), (c).end())

//repetition
//------------------------------------------
#define FOR(i, s, n) for (int i = s; i < (int)n; ++i)
#define REP(i, n) FOR(i, 0, n)
#define MOD 1000000007

#define rep(i, a, b) for (int i = a; i < (b); ++i)
#define trav(a, x) for (auto &a : x)
#define all(x) x.begin(), x.end()
#define sz(x) (int)(x).size()

typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
const double EPS = 1E-8;

#define chmin(x, y) x = min(x, y)
#define chmax(x, y) x = max(x, y)
const int INF = 100000000;

struct Edge
{
  int to, from;
  ll cost;
  Edge(int from, int to, ll cost) : from(from), to(to), cost(cost) {}
};

class UnionFind
{
public:
  vector<ll> par;
  vector<ll> siz;

  vector<ll> maxv;
  UnionFind(ll sz_) : par(sz_), siz(sz_, 1LL)
  {
    for (ll i = 0; i < sz_; ++i)
      par[i] = i;
  }
  void init(ll sz_)
  {
    par.resize(sz_);
    siz.assign(sz_, 1LL);
    for (ll i = 0; i < sz_; ++i)
      par[i] = i;
  }

  ll root(ll x)
  {
    while (par[x] != x)
    {
      x = par[x] = par[par[x]];
    }
    return x;
  }

  bool merge(ll x, ll y)
  {
    x = root(x);
    y = root(y);
    if (x == y)
      return false;
    if (siz[x] < siz[y])
      swap(x, y);
    siz[x] += siz[y];
    par[y] = x;
    return true;
  }

  bool issame(ll x, ll y)
  {
    return root(x) == root(y);
  }

  ll size(ll x)
  {
    return siz[root(x)];
  }
};

typedef vector<vector<Edge>> AdjList;
AdjList graph;

ll mod_pow(ll x, ll n, ll mod)
{
  ll res = 1;
  bool c = false;
  while (n)
  {
    if (n & 1)
      res = res * x;

    if (res > mod)
    {
      c = true;
      res %= mod;
    }
    x = x * x % mod;
    n >>= 1;
  }
  if (c)
    return mod;
  return res;
}

#define SIEVE_SIZE 5000000 + 10
bool sieve[SIEVE_SIZE];
void make_sieve()
{
  for (int i = 0; i < SIEVE_SIZE; ++i)
    sieve[i] = true;
  sieve[0] = sieve[1] = false;
  for (int i = 2; i * i < SIEVE_SIZE; ++i)
    if (sieve[i])
      for (int j = 2; i * j < SIEVE_SIZE; ++j)
        sieve[i * j] = false;
}

bool isprime(ll n)
{
  if (n == 0 || n == 1)
    return false;
  for (ll i = 2; i * i <= n; ++i)
    if (n % i == 0)
      return false;
  return true;
}

template <typename T>
vector<T> gauss_jordan(const vector<vector<T>> &A, const vector<T> &b)
{
  int n = A.size();
  vector<vector<T>> B(n, vector<T>(n + 1));

  for (int i = 0; i < n; ++i)
  {
    for (int j = 0; j < n; ++j)
    {
      B[i][j] = A[i][j];
    }
  }

  for (int i = 0; i < n; ++i)
    B[i][n] = b[i];

  for (int i = 0; i < n; ++i)
  {
    int pivot = i;
    for (int j = i; j < n; ++j)
    {
      if (abs(B[j][i]) > abs(B[pivot][i]))
        pivot = j;
    }
    swap(B[i], B[pivot]);

    if (abs(B[i][i]) < EPS)
      return vector<T>(); //解なし

    for (int j = i + 1; j <= n; ++j)
      B[i][j] /= B[i][i];
    for (int j = 0; j < n; ++j)
    {
      if (i != j)
      {
        for (int k = i + 1; k <= n; ++k)
          B[j][k] -= B[i][j] * B[i][k];
      }
    }
  }

  vector<T> x(n);

  for (int i = 0; i < n; ++i)
    x[i] = B[i][n];
  return x;
}

typedef vector<ll> vec;
typedef vector<vec> mat;

mat mul(mat &A, mat &B)
{
  mat C(A.size(), vec((int)B[0].size()));
  for (int i = 0; i < A.size(); ++i)
  {
    for (int k = 0; k < B.size(); ++k)
    {
      for (int j = 0; j < B[0].size(); ++j)
      {
        C[i][j] = (C[i][j] + A[i][k] * B[k][j] % MOD) % MOD;
      }
    }
  }
  return C;
}
mat mat_pow(mat A, ll n)
{
  mat B(A.size(), vec((int)A.size()));

  for (int i = 0; i < A.size(); ++i)
  {
    B[i][i] = 1;
  }

  while (n > 0)
  {
    if (n & 1)
      B = mul(B, A);
    A = mul(A, A);
    n >>= 1;
  }
  return B;
}

bool operator<(const pii &a, const pii &b)
{
  if (a.first == b.first)
    return a.second < b.second;
  return a.first < b.first;
}

const int MAX = 510000;
long long fac[MAX], finv[MAX], inv[MAX];

// テーブルを作る前処理
void COMinit()
{
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  for (int i = 2; i < MAX; i++)
  {
    fac[i] = fac[i - 1] * i % MOD;
    inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
    finv[i] = finv[i - 1] * inv[i] % MOD;
  }
}

// 二項係数計算
long long COM(int n, int k)
{
  if (n < k)
    return 0;
  if (n < 0 || k < 0)
    return 0;
  return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}

int bit[1000010];
int sums(int i)
{
  i++;
  int s = 0;
  while (i > 0)
  {
    s += bit[i];
    i -= i & -i;
  }
  return s;
}
void add(int i, int x)
{
  i++;
  while (i <= 1000010)
  {
    bit[i] += x;
    i += i & -i;
  }
}
long long extGCD(long long a, long long b, long long &x, long long &y)
{
  if (b == 0)
  {
    x = 1;
    y = 0;
    return a;
  }
  long long d = extGCD(b, a % b, y, x);
  y -= a / b * x;
  return d;
}

ll GCD(ll a, ll b)
{

  if (b == 0)
    return a;
  return GCD(b, a % b);
}

struct BipartiteMatching
{
  vector<vector<int>> graph;
  vector<int> match, alive, used;
  int timestamp;

  BipartiteMatching(int n) : graph(n), alive(n, 1), used(n, 0), match(n, -1), timestamp(0) {}

  void add_edge(int u, int v)
  {
    graph[u].push_back(v);
    graph[v].push_back(u);
  }

  bool dfs(int idx)
  {
    used[idx] = timestamp;
    for (auto &to : graph[idx])
    {
      int to_match = match[to];
      if (alive[to] == 0)
        continue;
      if (to_match == -1 || (used[to_match] != timestamp && dfs(to_match)))
      {
        match[idx] = to;
        match[to] = idx;
        return true;
      }
    }
    return false;
  }

  int bipartite_matching()
  {
    int ret = 0;
    for (int i = 0; i < graph.size(); i++)
    {
      if (alive[i] == 0)
        continue;
      if (match[i] == -1)
      {
        ++timestamp;
        ret += dfs(i);
      }
    }
    return ret;
  }

  void output()
  {
    for (int i = 0; i < graph.size(); i++)
    {
      if (i < match[i])
      {
        cout << i << "-" << match[i] << endl;
      }
    }
  }
};

int dp[200010];

bool used[200010];
int stock[200010];
int main()
{
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(15);

  int n, m;
  cin >> n >> m;

  vector<pair<int, int>> vp;
  for (int i = 0; i < m; i++)
  {
    int x, y;
    cin >> x >> y;
    vp.push_back({x, y});
  }
  for (int i = 1; i <= n; i++)
    dp[i] = 1;

  sort(all(vp));

  map<int, pair<int, int>> mp;
  for (int i = 0; i < vp.size(); i++)
  {
    int x = vp[i].first, y = vp[i].second;

    if (!used[y])
    {
      int t1 = dp[y], t2 = dp[y + 1];
      dp[y] += t2;
      dp[y + 1] += t1;
      mp[y] = make_pair(dp[y], dp[y + 1]);
      used[y] = true;
    }
    else
    {
      int sa1 = dp[y] - mp[y].first;
      int sa2 = dp[y + 1] - mp[y].second;

      dp[y + 1] += sa1;
      dp[y] += sa2;
      mp[y] = make_pair(dp[y], dp[y + 1]);
    }
  }
  for (int i = 1; i <= n; i++)
  {
    if (i - 1)
      cout << " ";

    cout << dp[i];
  }
  cout << endl;
  return 0;
}


```