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
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.StringTokenizer;
		public class Solution2{
			static int sum[] = new int[1000000];
			public static void main(String[] args) throws IOException{
				FastReader sc = new FastReader();
				long n = sc.nextLong();
				long k = sc.nextLong();
				long temp = n/2;
				if(temp/(k + 1) >= 1){
					long b = temp/(k+1);
					long a = k * b;
					System.out.println(b + " " + a + " " + (n - (a + b)));
				}else{
					System.out.println(0 + " " + 0 + " " + n);
				}
			}
			static class pair implements Comparable<pair>{
				String name;
				int score;
				public pair(String name, int score) {
					this.name = name;
					this.score = score;
				}
				
				public int compareTo(pair o ){
					return o.score - score;
				}
				
			}
			static class MyDs{
				ArrayList<Integer> arr;
				HashMap<Integer,LinkedList<Integer>> hmap;
				public MyDs(){
					arr = new ArrayList<Integer>();
					hmap = new HashMap<Integer,LinkedList<Integer>>();
				}
				void add(int x){
					if(!hmap.containsKey(x)){
						hmap.put(x,new LinkedList());
					}
					int s = arr.size();
					arr.add(x);
					hmap.get(x).add(s);
				}
				void remove(int x){
					if(!hmap.containsKey(x)){
						return;
					}
					Integer index = hmap.get(x).get(0);
					hmap.get(x).poll();
					int size = arr.size();
					Integer last = arr.get(arr.size() - 1);
					Collections.swap(arr,index,arr.size() - 1);
					arr.remove(size - 1);
					hmap.get(last).set(hmap.get(last).indexOf(size),index);
				}
				LinkedList<Integer> search(int x){
					return hmap.get(x);
				}
			}
			public static boolean compare(int[] arr,int[] arr2){
				boolean ans = true;
				for(int i = 0;i < 26;i++){
					if(arr[i] < arr2[i]){
						ans = false;
						break;
					}
				}
				return ans;
			}
			int gcd(int a, int b)
			{
			    if (b==0)
			        return a;
			    return gcd(b, a%b);
			}
			 
			 // Returns LCM of array elements
			static long findlcm(int arr[], int n)
			{
			    // Initialize result
			    long ans = arr[0];
			 
			    // ans contains LCM of arr[0],..arr[i]
			    // after i'th iteration,
			    for (int i=1; i<n; i++)
			        ans = ( ((arr[i]*ans)) /
			                (gcd(arr[i], ans)) );
			 
			    return ans;
			}
			public static boolean isPalindrome(String s){
				StringBuilder st = new StringBuilder(s);
				if(st.reverse().toString().equals(s)){
					return true;
				}
				return false;
			}
			public static int digits(int a){
				int count = 0;
				while(a != 0){
					count++;
					a = a/10;
				}
				return count;
			}
			public static long min(long n,long k){
				long ans = 0;
				long calc = n/k;
				long calc2 = n % k;
				long recalc = k - calc2;
				ans += calc * (calc - 1)/2 * recalc;
				ans += (calc + 1) * calc/2 * calc2;
				return ans;
			}
			public static long max(long n,long k){
				long ans = 0;
				long calc = n - k + 1;
				ans += calc * (calc - 1)/2;
				return ans;
			}
			public static boolean isOk(int[] arr,int size){
				if(size % 2 == 0){
					for(int i = 0;i < arr.length;i++){
						if(arr[i] % 2 != 0){
							return false;
						}
					}
					return true;
				}else{
					int count = 0;
					for(int i = 0;i < arr.length;i++){
						if(arr[i] % 2 != 0){
							count++;
						}
					}
					if(count > 1){
						return false;
					}
					return true;
				}
			}
			public static int complement(int index){
				if(index == 0){
					return 1;
				}
				return 0;
			}
			private static long gcd(long a, long b)
			{
			    while (b > 0)
			    {
			        long temp = b;
			        b = a % b; // % is remainder
			        a = temp;
			    }
			    return a;
			}
			void convertDegree(){
				
			}
			private static long gcd(long[] input)
			{
			    long result = input[0];
			    for(int i = 1; i < input.length; i++) result = gcd(result, input[i]);
			    return result;
			}
			private static long lcm(long a, long b)
			{
			    return a * (b / gcd(a, b));
			}
		
			private static long lcm(long[] input)
			{
			    long result = input[0];
			    for(int i = 1; i < input.length; i++) result = lcm(result, input[i]);
			    return result;
			}
			public static boolean[] sieveAlgo(int n){
				boolean isPrime[] = new boolean[n + 1];
				for (int i = 2; i <= n; i++) {
		            isPrime[i] = true;
		        }
		
		        // mark non-primes <= n using Sieve of Eratosthenes
		        for (int factor = 2; factor*factor <= n; factor++) {
		
		            // if factor is prime, then mark multiples of factor as nonprime
		            // suffices to consider mutiples factor, factor+1, ...,  n/factor
		            if (isPrime[factor]) {
		                for (int j = factor; factor*j <= n; j++) {
		                    isPrime[factor*j] = false;
		                }
		            }
		        }
		        return isPrime;
			}
			public static int binarySearch(int[] arr,int low,int high,int key){
				while(low <= high){
					int mid = (low + high)/2;
					if(arr[mid] == key){
						return mid;
					}else if(arr[mid] < key){
						low = mid + 1;
					}else{
						high = mid - 1;
					}
				}
				return -1;
			}
			public static int ternarySearch(int[] arr,int l,int r,int key){
				if(r >= l){
					int mid1 = l + (r-1)/3;
					int mid2 = r - (r-1)/3;
					if(arr[mid1] == key){
						return mid1;
					}else if(arr[mid2] == key){
						return mid2;
					}
					if(key < arr[mid1]){
						return ternarySearch(arr,l,mid1-1,key);
					}else if(key > arr[mid2]){
						return ternarySearch(arr,mid2 + 1,r,key);
					}else{
						return ternarySearch(arr,mid1 + 1,mid2 - 1,key);
					}
				}
				return -1;
			}
			public static double fun(double x){
				return 2 * x * x - 12 * x + 7;
			}
			
			public static double tsModified(double start,double end){
				double l = start;
				double r = end;
				for(int i = 0;i < 200;i++){
					double mid1 = (l * 2 + r)/3;
					double mid2 = (l + 2 * r)/3;
					if(fun(mid1) < fun(mid2)){
						r = mid2;
					}else{
						l = mid1;
					}
				}
				double x = l;
				return fun(x);
			}
			public static String fmt(double d)
			{
			    if(d == (long) d)
			        return String.format("%d",(long)d);
			    else
			        return String.format("%s",d);
			}
			public static String[][] comparator(String[][] arr){
				Arrays.sort(arr, new Comparator<String[]>() {
		            @Override
		            public int compare(String[] a,String[] b) {
		                Integer a1 = Integer.parseInt(a[1]);
		                Integer b1 = Integer.parseInt(b[1]);
		            	return b1.compareTo(a1);
		            }
		        });
				return arr;
			}
			public static StringBuilder[][] comparator2(StringBuilder[][] arr){
				Arrays.sort(arr, new Comparator<StringBuilder[]>() {
		            @Override
		            public int compare(StringBuilder[] a,StringBuilder[] b) {
		                StringBuilder a1 = a[0];
		                StringBuilder b1 = b[0];
		            	return a1.toString().compareTo(b1.toString());
		            }
		        });
				return arr;
			}
			public static int[][] comparator2(int[][] arr){
				Arrays.sort(arr, new Comparator<int[]>() {
		            @Override
		            public int compare(int[] a,int[] b) {
		                Integer a1 = a[0];
		                Integer b1 = b[0];
		            	return b1.compareTo(a1);
		            }
		        });
				return arr;
			}
			static class FastReader
		    {
		        BufferedReader br;
		        StringTokenizer st;
		 
		        public FastReader()
		        {
		            br = new BufferedReader(new
		                     InputStreamReader(System.in));
		        }
		 
		        String next()
		        {
		            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());
		        }
		 
		        long nextLong()
		        {
		            return Long.parseLong(next());
		        }
		 
		        double nextDouble()
		        {
		            return Double.parseDouble(next());
		        }
		 
		        String nextLine()
		        {
		            String str = "";
		            try
		            {
		                str = br.readLine();
		            }
		            catch (IOException e)
		            {
		                e.printStackTrace();
		            }
		            return str;
		        }
		    }
			public static String min(int m,int n){
				int[] arr = new int[m];
				arr[0] = 1;
				int sum = 1;
				int j = m - 1;
				for(int i = 1;i <= 18* m + 10;i++){
					if(sum != n){
						if(arr[j] == 9){
							j--;
						}else{
							arr[j]++;
							sum++;
						}
					}
					else{
						break;
					}
				}
				StringBuilder min = new StringBuilder("");
				for(int i = 0;i < arr.length;i++){
					min.append(arr[i]);
				}
				return min.toString();
			}
			
			public static String max(int m,int n){
				int[] arr = new int[m];
				arr[0] = 1;
				int sum = 1;
				int j = 0;
				for(int i = 1;i <= 9 * m + 10;i++){
					if(sum != n){
						if(arr[j] == 9){
							j++;
						}else{
							arr[j]++;
							sum++;
						}
					}
					else{
						break;
					}
				}
				StringBuilder min = new StringBuilder("");
				for(int i = 0;i < arr.length;i++){
					min.append(arr[i]);
				}
				return min.toString();
			}
		    public static int KMPSearch(String txt,String pat){
				int m = pat.length();
				int n = txt.length();
				int lps[] = new int[m];
				int j = 0;
				int count = 0;
				PrefixTable(pat,m,lps);
				int i = 0;
				while (i < n)
			        {
			            if (pat.charAt(j) == txt.charAt(i))
			            {
			                j++;
			                i++;
			            }
			            if (j == m)
			            {
			            	count++;
			                j = lps[j-1];
			            }
			            else if (i < n && pat.charAt(j) != txt.charAt(i))
			            {
			                if (j != 0)
			                    j = lps[j-1];
			                else
			                    i = i+1;
			            }
			        }
				return count;
			}
			public static void PrefixTable(String pat,int m,int[] lps){
				int len = 0;
				int i = 1;
				lps[0] = 0;
				while(i < m){
					if(pat.charAt(i) == pat.charAt(len)){
						lps[i] = len + 1;
						i++;
						len++;
					}else if(len > 0){
						len = lps[len - 1];
					}else{
						lps[i] = 0;
						i++;
					}
				}
			}
		    public int digit(int x){
		    	int temp = x;
		    	int count = 0;
		    	while(temp != 0){
		    		count++;
		    		temp = temp/10;
		    	}
		    	return count;
		    }
		    public int sum(int x){
		    	int temp = x;
		    	int count = 0;
		    	while(temp != 0){
		    		count += temp % 10;
		    		temp = temp/10;
		    	}
		    	return count;
		    }
		    public int product(int x){
		    	int temp = x;
		    	int count = 1;
		    	while(temp != 0){
		    		count*=temp % 10;
		    		temp = temp/10;
		    	}
		    	return count;
		    }
		    public boolean isValid2(int x){
		    	int temp = x;
		    	while(temp != 0){
		    		if(temp % 10 == 0){
		    			return false;
		    		}
		    		temp = temp/10;
		    	}
		    	return true;
		    }
		    public boolean isValid(int x){
		    	if(!isValid2(x)){
		    		return false;
		    	}else{
		    		if(product(x) <= sum(x)){
		    			return true;
		    		}
		    		return false; 
		    	}
		    }
		}