Problem: Input

The input is given from Standard Input in the following format:


> $N \ Q$ $a_1 \ b_1$ $a_2 \ b_2$ $ ： \ ： $ $a_Q \ b_Q$

Output

* You have to print $N$ lines.
* The $i$-th line should contain the number of dishes of sushi had eaten for customer $i (1 \le i \le N)$.



Constraints

* $3 \le N, Q \le 100,000$
* $1 \le a_i \le N$
* $1 \le b_i \le 10^{12}$
* Any final results do not exceed $2 \times 10^{13}$.



Subtasks

Subtask 1 [ $60$ points ]


* $N, Q \le 100$
* $b_i = 1$

Subtask 2 [ $400$ points ]


* $N, Q \le 100$
* $b_i \le 10^{12}$

Subtask 3 [ $240$ points ]


* $N, Q \le 100,000$
* $b_i = 1$

Subtask 4 [ $500$ points ]


* There are no additional constraints.

Output

* You have to print $N$ lines.
* The $i$-th line should contain the number of dishes of sushi had eaten for customer $i (1 \le i \le N)$.



Constraints

* $3 \le N, Q \le 100,000$
* $1 \le a_i \le N$
* $1 \le b_i \le 10^{12}$
* Any final results do not exceed $2 \times 10^{13}$.



Subtasks

Subtask 1 [ $60$ points ]


* $N, Q \le 100$
* $b_i = 1$

Subtask 2 [ $400$ points ]


* $N, Q \le 100$
* $b_i \le 10^{12}$

Subtask 3 [ $240$ points ]


* $N, Q \le 100,000$
* $b_i = 1$

Subtask 4 [ $500$ points ]


* There are no additional constraints.

Input

The input is given from Standard Input in the following format:


> $N \ Q$ $a_1 \ b_1$ $a_2 \ b_2$ $ ： \ ： $ $a_Q \ b_Q$

Examples

Input

9 3
5 11
8 4
4 7


Output

4
4
4
4
2
2
1
1
0


Input

6 6
3 5
6 11
1 6
4 7
5 2
2 5


Output

10
10
5
5
4
2


Input

5 6
1 1
2 1
3 1
1 1
5 1
3 1


Output

2
2
1
1
0


Input

10 10
10 10
9 20
8 30
7 40
6 50
5 60
4 70
3 80
2 90
1 100


Output

223
123
77
50
33
21
12
7
3
1

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
using Int = long long;

template <typename T,typename E>
struct SegmentTree{
  using F = function<T(T,T)>;
  using G = function<T(T,E)>;
  using H = function<E(E,E)>;
  using P = function<E(E,size_t)>;
  Int n;
  F f;
  G g;
  H h;
  T ti;
  E ei;
  P p;
  vector<T> dat;
  vector<E> laz;
  SegmentTree(Int n_,F f,G g,H h,T ti,E ei,
	      P p=[](E a,size_t b){b++;return a;}):
    f(f),g(g),h(h),ti(ti),ei(ei),p(p){
    init(n_);
  }
  void init(Int n_){
    n=1;
    while(n<n_) n*=2;
    dat.assign(2*n-1,ti);
    laz.assign(2*n-1,ei);
  }
  void build(Int n_, vector<T> v){
    for(Int i=0;i<n_;i++) dat[i+n-1]=v[i];
    for(Int i=n-2;i>=0;i--)
      dat[i]=f(dat[i*2+1],dat[i*2+2]);
  }
  inline void eval(Int len,Int k){
    if(laz[k]==ei) return;
    if(k*2+1<n*2-1){
      laz[k*2+1]=h(laz[k*2+1],laz[k]);
      laz[k*2+2]=h(laz[k*2+2],laz[k]);
    }
    dat[k]=g(dat[k],p(laz[k],len));
    laz[k]=ei;
  }
  T update(Int a,Int b,E x,Int k,Int l,Int r){
    eval(r-l,k);
    if(r<=a||b<=l) return dat[k];
    if(a<=l&&r<=b){
      laz[k]=h(laz[k],x);
      return g(dat[k],p(laz[k],r-l));
    }
    return dat[k]=f(update(a,b,x,k*2+1,l,(l+r)/2),
		    update(a,b,x,k*2+2,(l+r)/2,r));
  }
  T update(Int a,Int b,E x){
    return update(a,b,x,0,0,n);
  }
  T query(Int a,Int b,Int k,Int l,Int r){
    eval(r-l,k);
    if(r<=a||b<=l) return ti;
    if(a<=l&&r<=b) return dat[k];
    T vl=query(a,b,k*2+1,l,(l+r)/2);
    T vr=query(a,b,k*2+2,(l+r)/2,r);
    return f(vl,vr);
  }
  T query(Int a,Int b){
    return query(a,b,0,0,n);
  }
  void update(Int k,T x){
    query(k,k+1);//evaluate
    k+=n-1;
    dat[k]=x;
    while(k){
      k=(k-1)/2;
      dat[k]=f(dat[k*2+1],dat[k*2+2]);
    }
  }
};

//INSERT ABOVE HERE
signed main(){
  Int n,q;
  cin>>n>>q;

  auto f=[](Int a,Int b){return a+b;};
  auto g=[](Int a,Int b){a++;return b;};
  auto p=[](Int a,size_t b){return a*b;};

  SegmentTree<Int, Int> seg(n,f,g,g,0,0,p);

  for(Int i=0;i<q;i++){
    Int a,b;
    cin>>a>>b;

    Int l=-1,r=a;
    while(l+1<r){
      Int m=(l+r)>>1;
      Int k=seg.query(m,m+1);
      if(k*(a-m)<=seg.query(m,a)+b) r=m;
      else l=m;
    }
    
    Int k=seg.query(r,r+1);
    b-=k*(a-r)-seg.query(r,a);
    seg.update(r,a,k);
    k+=b/(a-r);b%=(a-r);
    seg.update(r,a,k);
    seg.update(r,r+b,k+1);

    continue;
    cout<<r<<":"<<a<<":"<<b<<endl;
    for(Int j=0;j<n;j++)
      cout<<seg.query(j,j+1)<<" ";
    cout<<endl;
  }
  
  for(Int i=0;i<n;i++)
    cout<<seg.query(i,i+1)<<endl;
  
  return 0;
}