#include <bits/stdc++.h>
#pragma GCC optimize("O3")
using namespace std;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
int scan() { return getchar(); }
void scan(int& a) { cin >> a; }
void scan(long long& a) { cin >> a; }
void scan(char& a) { cin >> a; }
void scan(double& a) { cin >> a; }
void scan(long double& a) { cin >> a; }
void scan(char a[]) { scanf("%s", a); }
void scan(string& a) { cin >> a; }
template <class T>
void scan(vector<T>&);
template <class T, size_t size>
void scan(array<T, size>&);
template <class T, class L>
void scan(pair<T, L>&);
template <class T, size_t size>
void scan(T (&)[size]);
template <class T>
void scan(vector<T>& a) {
  for (auto& i : a) scan(i);
}
template <class T>
void scan(deque<T>& a) {
  for (auto& i : a) scan(i);
}
template <class T, size_t size>
void scan(array<T, size>& a) {
  for (auto& i : a) scan(i);
}
template <class T, class L>
void scan(pair<T, L>& p) {
  scan(p.first);
  scan(p.second);
}
template <class T, size_t size>
void scan(T (&a)[size]) {
  for (auto& i : a) scan(i);
}
template <class T>
void scan(T& a) {
  cin >> a;
}
void IN() {}
template <class Head, class... Tail>
void IN(Head& head, Tail&... tail) {
  scan(head);
  IN(tail...);
}
string stin() {
  string s;
  cin >> s;
  return s;
}
template <class T>
inline bool chmax(T& a, T b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
inline bool chmin(T& a, T b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
vector<int> iota(int n) {
  vector<int> a(n);
  iota(begin(a), end(a), 0);
  return a;
}
template <class T>
void UNIQUE(vector<T>& x) {
  sort(begin(x), end(x));
  x.erase(unique(begin(x), end(x)), x.end());
}
int in() {
  int x;
  cin >> x;
  return x;
}
long long lin() {
  unsigned long long x;
  cin >> x;
  return x;
}
void print() { putchar(' '); }
void print(bool a) { cout << a; }
void print(int a) { cout << a; }
void print(long long a) { cout << a; }
void print(char a) { cout << a; }
void print(string& a) { cout << a; }
void print(double a) { cout << a; }
template <class T>
void print(const vector<T>&);
template <class T, size_t size>
void print(const array<T, size>&);
template <class T, class L>
void print(const pair<T, L>& p);
template <class T, size_t size>
void print(const T (&)[size]);
template <class T>
void print(const vector<T>& a) {
  if (a.empty()) return;
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    cout << " ";
    print(*i);
  }
  cout << endl;
}
template <class T>
void print(const deque<T>& a) {
  if (a.empty()) return;
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    cout << " ";
    print(*i);
  }
}
template <class T, size_t size>
void print(const array<T, size>& a) {
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    cout << " ";
    print(*i);
  }
}
template <class T, class L>
void print(const pair<T, L>& p) {
  cout << '(';
  print(p.first);
  cout << ",";
  print(p.second);
  cout << ')';
}
template <class T, size_t size>
void print(const T (&a)[size]) {
  print(a[0]);
  for (auto i = a; ++i != end(a);) {
    cout << " ";
    print(*i);
  }
}
template <class T>
void print(const T& a) {
  cout << a;
}
int out() {
  putchar('\n');
  return 0;
}
template <class T>
int out(const T& t) {
  print(t);
  putchar('\n');
  return 0;
}
template <class Head, class... Tail>
int out(const Head& head, const Tail&... tail) {
  print(head);
  putchar(' ');
  out(tail...);
  return 0;
}
long long gcd(long long a, long long b) {
  while (b) {
    long long c = b;
    b = a % b;
    a = c;
  }
  return a;
}
long long lcm(long long a, long long b) {
  if (!a || !b) return 0;
  return a * b / gcd(a, b);
}
vector<pair<long long, long long>> factor(long long x) {
  vector<pair<long long, long long>> ans;
  for (long long i = 2; i * i <= x; i++)
    if (x % i == 0) {
      ans.push_back({i, 1});
      while ((x /= i) % i == 0) ans.back().second++;
    }
  if (x != 1) ans.push_back({x, 1});
  return ans;
}
vector<int> divisor(int x) {
  vector<int> ans;
  for (int i = 1; i * i <= x; i++)
    if (x % i == 0) {
      ans.push_back(i);
      if (i * i != x) ans.push_back(x / i);
    }
  return ans;
}
int popcount(long long x) { return __builtin_popcountll(x); }
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int rnd(int n) { return uniform_int_distribution<int>(0, n)(rng); }
template <class... T>
void err(const T&...) {}
struct UnionFind {
  vector<int> data;
  UnionFind(int sz) { data.assign(sz, -1); }
  bool unite(int x, int y) {
    x = find(x), y = find(y);
    if (x == y) return (false);
    if (data[x] > data[y]) swap(x, y);
    data[x] += data[y];
    data[y] = x;
    return (true);
  }
  int find(int k) {
    if (data[k] < 0) return (k);
    return (data[k] = find(data[k]));
  }
  int size(int k) { return (-data[find(k)]); }
};
long long extgcd(long long a, long long b, long long& p, long long& q) {
  if (!b) {
    p = 1;
    q = 0;
    return a;
  }
  long long d = extgcd(b, a % b, q, p);
  q -= a / b * p;
  return d;
}
signed main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  cout << fixed << setprecision(15);
  long long T, n;
  IN(T, n);
  vector<long long> a(n);
  IN(a);
  long long A = accumulate(begin(a), end(a), 0LL);
  vector<long long> b{a[0]};
  for (long long i = 1; i <= n - 1; ++i) b.push_back(b.back() + a[i]);
  A %= T;
  long long g = gcd(A, T);
  map<long long, vector<pair<long long, int>>> mp;
  set<int> second;
  for (long long i = 0; i < n; ++i) {
    b[i] %= T;
    if (second.count(b[i])) continue;
    mp[b[i] % g].emplace_back(b[i] / g, i);
    second.emplace(b[i]);
  }
  long long p, q;
  extgcd(A, T, p, q);
  vector<long long> ans(n);
  for (auto [e, v] : mp) {
    for (auto& P : v) {
      (P.first *= p) %= (T / g);
    }
    sort(begin(v), end(v));
    v.push_back(*v.begin());
    for (long long i = 0; i < v.size() - 1; ++i) {
      ans[v[i].second] = (v[i + 1].first - v[i].first + (T / g)) % (T / g);
    }
    if (v.size() == 2) ans[v[0].second] = T / g;
  }
  print(ans);
}

### Prompt

Develop a solution in cpp to the problem described below:

After studying the beacons Mister B decided to visit alien's planet, because he learned that they live in a system of flickering star Moon. Moreover, Mister B learned that the star shines once in exactly T seconds. The problem is that the star is yet to be discovered by scientists.

There are n astronomers numerated from 1 to n trying to detect the star. They try to detect the star by sending requests to record the sky for 1 second. 

The astronomers send requests in cycle: the i-th astronomer sends a request exactly ai second after the (i - 1)-th (i.e. if the previous request was sent at moment t, then the next request is sent at moment t + ai); the 1-st astronomer sends requests a1 seconds later than the n-th. The first astronomer sends his first request at moment 0.

Mister B doesn't know the first moment the star is going to shine, but it's obvious that all moments at which the star will shine are determined by the time of its shine moment in the interval [0, T). Moreover, this interval can be split into T parts of 1 second length each of form [t, t + 1), where t = 0, 1, 2, ..., (T - 1).

Mister B wants to know how lucky each astronomer can be in discovering the star first.

For each astronomer compute how many segments of form [t, t + 1) (t = 0, 1, 2, ..., (T - 1)) there are in the interval [0, T) so that this astronomer is the first to discover the star if the first shine of the star happens in this time interval.

Input

The first line contains two integers T and n (1 ≤ T ≤ 109, 2 ≤ n ≤ 2·105).

The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109).

Output

Print n integers: for each astronomer print the number of time segments describer earlier.

Examples

Input

4 2
2 3


Output

3 1 


Input

5 4
1 1 1 1


Output

2 1 1 1 

Note

In the first sample test the first astronomer will send requests at moments t1 = 0, 5, 10, ..., the second — at moments t2 = 3, 8, 13, .... That's why interval [0, 1) the first astronomer will discover first at moment t1 = 0, [1, 2) — the first astronomer at moment t1 = 5, [2, 3) — the first astronomer at moment t1 = 10, and [3, 4) — the second astronomer at moment t2 = 3.

In the second sample test interval [0, 1) — the first astronomer will discover first, [1, 2) — the second astronomer, [2, 3) — the third astronomer, [3, 4) — the fourth astronomer, [4, 5) — the first astronomer.

### Response

```cpp
#include <bits/stdc++.h>
#pragma GCC optimize("O3")
using namespace std;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
int scan() { return getchar(); }
void scan(int& a) { cin >> a; }
void scan(long long& a) { cin >> a; }
void scan(char& a) { cin >> a; }
void scan(double& a) { cin >> a; }
void scan(long double& a) { cin >> a; }
void scan(char a[]) { scanf("%s", a); }
void scan(string& a) { cin >> a; }
template <class T>
void scan(vector<T>&);
template <class T, size_t size>
void scan(array<T, size>&);
template <class T, class L>
void scan(pair<T, L>&);
template <class T, size_t size>
void scan(T (&)[size]);
template <class T>
void scan(vector<T>& a) {
  for (auto& i : a) scan(i);
}
template <class T>
void scan(deque<T>& a) {
  for (auto& i : a) scan(i);
}
template <class T, size_t size>
void scan(array<T, size>& a) {
  for (auto& i : a) scan(i);
}
template <class T, class L>
void scan(pair<T, L>& p) {
  scan(p.first);
  scan(p.second);
}
template <class T, size_t size>
void scan(T (&a)[size]) {
  for (auto& i : a) scan(i);
}
template <class T>
void scan(T& a) {
  cin >> a;
}
void IN() {}
template <class Head, class... Tail>
void IN(Head& head, Tail&... tail) {
  scan(head);
  IN(tail...);
}
string stin() {
  string s;
  cin >> s;
  return s;
}
template <class T>
inline bool chmax(T& a, T b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
inline bool chmin(T& a, T b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
vector<int> iota(int n) {
  vector<int> a(n);
  iota(begin(a), end(a), 0);
  return a;
}
template <class T>
void UNIQUE(vector<T>& x) {
  sort(begin(x), end(x));
  x.erase(unique(begin(x), end(x)), x.end());
}
int in() {
  int x;
  cin >> x;
  return x;
}
long long lin() {
  unsigned long long x;
  cin >> x;
  return x;
}
void print() { putchar(' '); }
void print(bool a) { cout << a; }
void print(int a) { cout << a; }
void print(long long a) { cout << a; }
void print(char a) { cout << a; }
void print(string& a) { cout << a; }
void print(double a) { cout << a; }
template <class T>
void print(const vector<T>&);
template <class T, size_t size>
void print(const array<T, size>&);
template <class T, class L>
void print(const pair<T, L>& p);
template <class T, size_t size>
void print(const T (&)[size]);
template <class T>
void print(const vector<T>& a) {
  if (a.empty()) return;
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    cout << " ";
    print(*i);
  }
  cout << endl;
}
template <class T>
void print(const deque<T>& a) {
  if (a.empty()) return;
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    cout << " ";
    print(*i);
  }
}
template <class T, size_t size>
void print(const array<T, size>& a) {
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    cout << " ";
    print(*i);
  }
}
template <class T, class L>
void print(const pair<T, L>& p) {
  cout << '(';
  print(p.first);
  cout << ",";
  print(p.second);
  cout << ')';
}
template <class T, size_t size>
void print(const T (&a)[size]) {
  print(a[0]);
  for (auto i = a; ++i != end(a);) {
    cout << " ";
    print(*i);
  }
}
template <class T>
void print(const T& a) {
  cout << a;
}
int out() {
  putchar('\n');
  return 0;
}
template <class T>
int out(const T& t) {
  print(t);
  putchar('\n');
  return 0;
}
template <class Head, class... Tail>
int out(const Head& head, const Tail&... tail) {
  print(head);
  putchar(' ');
  out(tail...);
  return 0;
}
long long gcd(long long a, long long b) {
  while (b) {
    long long c = b;
    b = a % b;
    a = c;
  }
  return a;
}
long long lcm(long long a, long long b) {
  if (!a || !b) return 0;
  return a * b / gcd(a, b);
}
vector<pair<long long, long long>> factor(long long x) {
  vector<pair<long long, long long>> ans;
  for (long long i = 2; i * i <= x; i++)
    if (x % i == 0) {
      ans.push_back({i, 1});
      while ((x /= i) % i == 0) ans.back().second++;
    }
  if (x != 1) ans.push_back({x, 1});
  return ans;
}
vector<int> divisor(int x) {
  vector<int> ans;
  for (int i = 1; i * i <= x; i++)
    if (x % i == 0) {
      ans.push_back(i);
      if (i * i != x) ans.push_back(x / i);
    }
  return ans;
}
int popcount(long long x) { return __builtin_popcountll(x); }
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int rnd(int n) { return uniform_int_distribution<int>(0, n)(rng); }
template <class... T>
void err(const T&...) {}
struct UnionFind {
  vector<int> data;
  UnionFind(int sz) { data.assign(sz, -1); }
  bool unite(int x, int y) {
    x = find(x), y = find(y);
    if (x == y) return (false);
    if (data[x] > data[y]) swap(x, y);
    data[x] += data[y];
    data[y] = x;
    return (true);
  }
  int find(int k) {
    if (data[k] < 0) return (k);
    return (data[k] = find(data[k]));
  }
  int size(int k) { return (-data[find(k)]); }
};
long long extgcd(long long a, long long b, long long& p, long long& q) {
  if (!b) {
    p = 1;
    q = 0;
    return a;
  }
  long long d = extgcd(b, a % b, q, p);
  q -= a / b * p;
  return d;
}
signed main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  cout << fixed << setprecision(15);
  long long T, n;
  IN(T, n);
  vector<long long> a(n);
  IN(a);
  long long A = accumulate(begin(a), end(a), 0LL);
  vector<long long> b{a[0]};
  for (long long i = 1; i <= n - 1; ++i) b.push_back(b.back() + a[i]);
  A %= T;
  long long g = gcd(A, T);
  map<long long, vector<pair<long long, int>>> mp;
  set<int> second;
  for (long long i = 0; i < n; ++i) {
    b[i] %= T;
    if (second.count(b[i])) continue;
    mp[b[i] % g].emplace_back(b[i] / g, i);
    second.emplace(b[i]);
  }
  long long p, q;
  extgcd(A, T, p, q);
  vector<long long> ans(n);
  for (auto [e, v] : mp) {
    for (auto& P : v) {
      (P.first *= p) %= (T / g);
    }
    sort(begin(v), end(v));
    v.push_back(*v.begin());
    for (long long i = 0; i < v.size() - 1; ++i) {
      ans[v[i].second] = (v[i + 1].first - v[i].first + (T / g)) % (T / g);
    }
    if (v.size() == 2) ans[v[0].second] = T / g;
  }
  print(ans);
}

```