There are n students who have taken part in an olympiad. Now it's time to award the students.

Some of them will receive diplomas, some wiil get certificates, and others won't receive anything. Students with diplomas and certificates are called winners. But there are some rules of counting the number of diplomas and certificates. The number of certificates must be exactly k times greater than the number of diplomas. The number of winners must not be greater than half of the number of all students (i.e. not be greater than half of n). It's possible that there are no winners.

You have to identify the maximum possible number of winners, according to these rules. Also for this case you have to calculate the number of students with diplomas, the number of students with certificates and the number of students who are not winners.

Input

The first (and the only) line of input contains two integers n and k (1 ≤ n, k ≤ 1012), where n is the number of students and k is the ratio between the number of certificates and the number of diplomas.

Output

Output three numbers: the number of students with diplomas, the number of students with certificates and the number of students who are not winners in case when the number of winners is maximum possible.

It's possible that there are no winners.

Examples

Input

18 2


Output

3 6 9


Input

9 10


Output

0 0 9


Input

1000000000000 5


Output

83333333333 416666666665 500000000002


Input

1000000000000 499999999999


Output

1 499999999999 500000000000
//********************(Writer-Aagam)*******************************
//*******************(User-getlost01)******************************

import java.util.*;
import java.lang.*;
import java.io.*;
import java.math.BigInteger;

//------------------------Main_class-------------------------------

public class Codechef
{
static AagamReader ar=new AagamReader();
   
//----------------------Main_Function------------------------------

public static void main (String[] args) throws java.lang.Exception
{
// long start=System.currentTimeMillis();

long n=ar.nextLong();
long k=ar.nextLong();
// long a=n/2;
long a=n/(2*(k+1));
long b=a*k;
System.out.println(a+" "+b+" "+(n-a-b));
           
// long end=System.currentTimeMillis();
// System.out.println(end-start+" Millisec");
}

//--------------------Solving_Function---------------------------

static void solve(String s)
{


System.out.println(s);
}
//------------------------Reverse----------------------------------

public static int[] reverses(int data[], int left, int right)
{
while (left < right) 
{
int temp = data[left];
data[left++] = data[right];
data[right--] = temp;
}
return data;
}

//----------------------------Swap-----------------------------------

public static int[] swap(int data[], int left, int right) 
{
int temp = data[left];
data[left] = data[right];
data[right] = temp;
return data;
}

//--------------------------Factorial---------------------------------

public static long factorials(long n)
{
if(n==0) return 1; 

return n*factorials(n-1);
}

//-------------------------G.C.D---------------------------------------

public static long gcd(long a,long b)
{
if(b==0) return a;

return gcd(b,a%b);
}

//-------------------------ModularG.C.D-------------------------------

static long gcd(long a,long b,long n,long mod)
{
if(a==b)
return (mod_expo(a,n,mod)+mod_expo(b,n,mod))%mod;

long c=1;long diff=a-b;

for(long i=1;i<=Math.sqrt(diff);i++)
{
if(diff%i==0)
{
long temp=(mod_expo(a,n,i)+mod_expo(b,n,i))%i;
if(temp==0)
c=Math.max(c,i);

temp=(mod_expo(a,n,diff/i)+mod_expo(b,n,diff/i))%(diff/i);
if(temp==0)
c=Math.max(c,diff/i);
}
}
return c%mod;
}

//------------------------ l.C.M--------------------------------------
public static long lcm(long a,long b)
{
return (a*b)/gcd(a,b);
}
//---------------------------Prime-----------------------------------

public static boolean[] seive(int n)
{
boolean isPrime[]=new boolean[n+1];
Arrays.fill(isPrime,true);
isPrime[0]=false;
isPrime[1]=false;
for(int i=2;i*i<=n;i++)
{
for(int j=2*i;j<=n;j+=i)
{
isPrime[j]=false;
}
}
return isPrime;
}

//----------------------Modular_Exponentiation-------------------------

static long mod_expo(long a,long b,long n)
{
long res=1;
while(b>0)
{
if((b&1)!=0)
{res=(res*a%n)%n;}

a=(a%n*a%n)%n;
b=b>>1;
}
return res;
}

//-------------------------Power-----------------------------------------

static int fastpower(int a,int b)
{
int res=1;
while(b>0)
{
if((b&1)!=0)
res=res*a;

a=a*a;
b=b>>1;
}
return res;
}

//---------------------Modular_Arithmetic---------------------------------

public long modularSubtraction(long a,long b,long MOD)    // Modular Subtraction
{ return (a%MOD-b%MOD+MOD)%MOD; }

public long modularMultiplication(long a,long b,long MOD) // Modular Multiplication
{ return ((a%MOD)*(b%MOD))%MOD; }

public long modularAddition(long a,long b,long MOD)       // Modular Addition
{ return (a%MOD+b%MOD)%MOD; }	

//-----------------------Binary_Searching-----------------------------------

public static int binarySearch(int arr[], int first, int last, int num)
{
int mid = (first + last) / 2;
while (first <= last)
{
if (arr[mid] < num) {first = mid + 1;} 
else if (arr[mid] == num) {return mid;}
else {last = mid - 1;}
mid = (first + last) / 2;
}
return -1;
}

//-------------------------------------Node-------------------------------- 

static class Node<E>             
{
protected E data;
protected Node link;  //link====>next/linked address

public Node() {data=null; link=null;}

public Node(E d,Node n) {data=d; link=n;}  

public void setLink(Node n) {link=n;}

public void setData(E d) {data=d;}

public Node getLink() {return link;}

public E getData() {return data;}
}

//--------------------------------------Aaagmlist-----------------------------

static class aagamList<E>
{
protected Node start;
protected Node end;
public int size;

public aagamList() {start=null;end=null;size=0;}

public boolean isEmpty() {return start==null;}

public int size() {return size;}

public E get(int pos)
{ Node<E> curr=start; int c=0;
  while(curr!=null) {if(c==pos) return curr.data; c++; curr=curr.link;}
  return null;}

public void push_lr(E val) { Node<E> cnode=new Node<>(val,null); cnode.link=start; start=cnode;}

public void prepend(E val)
{ Node<E> cnode=new Node<E>(val,null); size++;
  if(start==null) {start=cnode;end=start;} 
  else {cnode.setLink(start);start=cnode;}
}

public void append(E val)
{ Node<E> cnode=new Node<E>(val,null); size++;
  if(start==null) {start=cnode;end=start;} 
  else {end.setLink(cnode);end=cnode;}
}

public void insert(E val,int pos)
{ Node<E> cnode=new Node<>(val,null); Node temp=start; --pos;
  for(int i=1;i<size;i++)
  { if(i==pos) {Node tmp=temp.getLink(); temp.setLink(cnode); cnode.setLink(tmp); break;}
    temp=temp.getLink(); } size++;
}

public void remove(int pos)
{ if(pos==1) {start=start.getLink(); size--; return;}
  if(pos==size) {Node s=start; Node t=start; while(s!=end) {t=s; s=s.getLink();}
  end=t; end.setLink(null); size--; return;}
  Node temp=start; --pos;
  for(int i=0;i<size-1;i++) 
  { if(i==pos) {Node tmp=temp.getLink(); tmp=tmp.getLink(); temp.setLink(tmp); break;}
  temp=temp.getLink(); }size--; 
}

public void display()
{ if(size==0) {System.out.println(" "); return;}
  if(start.getLink()==null) {System.out.println(start.getData()); return;}
  Node<E> temp=start; System.out.print(temp.getData()+" ");
  temp=start.getLink();
  while(temp.getLink()!=null) {System.out.print(temp.getData()+" "); temp=temp.getLink();}
  System.out.print(temp.getData()+"\n");
}
}

//----------------------------------------Stack------------------------------

static class Astack<E>
{
aagamList<E> a=new aagamList<>();
public void push(E val) {a.append(val); return;}
public void pop() {a.remove(a.size()-1); return;}
public void display() {a.display(); return;}
}

//---------------------------------------Dequeue------------------------------

static class Adequeue<E>
{
aagamList<E> a=new aagamList<>();
public void push_f(E val) {a.prepend(val); return;}
public void push_b(E val) {a.append(val); return;}
public void pop_f() {a.remove(0); return;}
public void pop_b() {a.remove(a.size()-1); return;}
public void display() {a.display(); return;}
}

//-----------------------AagamReader_class------------------------------------

public static class AagamReader 
{
BufferedReader br;
StringTokenizer st;

public AagamReader()
{
br = new BufferedReader(new InputStreamReader(System.in));
}

String next()                                           //ReadNextToken
{
while (st == null || !st.hasMoreElements()) 
{
try 
{
st = new StringTokenizer(br.readLine());
}
catch (IOException e) {e.printStackTrace();}
}
return st.nextToken();
}

int nextInt() { return Integer.parseInt(next()); }        //ReadInt

long nextLong() { return Long.parseLong(next()); }        //ReadLong

double nextDouble() { return Double.parseDouble(next());} //ReadDouble

int[] get_arr(int n)                                      //ReadArray
{
int arr[]=new int [n];
for(int i=0;i<n;i++)
arr[i]= Integer.parseInt(next());
return arr;
}

String nextLine()                                         //Readline
{
String str = "";
try 
{ 
str = br.readLine(); 
}
catch (IOException e) 
{
e.printStackTrace();
}
return str;
}
}
}
//=>->->->-->->->-[>>>>>>ENDING_WITH_HAPPY_CODING<<<<<<]-<-<-<-<-<-<-<-<-<-<=

