Okabe needs bananas for one of his experiments for some strange reason. So he decides to go to the forest and cut banana trees.

Consider the point (x, y) in the 2D plane such that x and y are integers and 0 ≤ x, y. There is a tree in such a point, and it has x + y bananas. There are no trees nor bananas in other points. Now, Okabe draws a line with equation <image>. Okabe can select a single rectangle with axis aligned sides with all points on or under the line and cut all the trees in all points that are inside or on the border of this rectangle and take their bananas. Okabe's rectangle can be degenerate; that is, it can be a line segment or even a point.

Help Okabe and find the maximum number of bananas he can get if he chooses the rectangle wisely.

Okabe is sure that the answer does not exceed 1018. You can trust him.

Input

The first line of input contains two space-separated integers m and b (1 ≤ m ≤ 1000, 1 ≤ b ≤ 10000).

Output

Print the maximum number of bananas Okabe can get from the trees he cuts.

Examples

Input

1 5


Output

30


Input

2 3


Output

25

Note

<image>

The graph above corresponds to sample test 1. The optimal rectangle is shown in red and has 30 bananas.
import java.util.*;

import java.io.*;
import java.math.*;
 public class Q1 {

	static ArrayList<Integer> adj[],adj2[];
	static int color[],cc;
	static long mod=1000000007;
	static TreeSet<Integer> ts;
	static boolean b[],visited[],possible,ans1,ans2;
	static Stack<Integer> s;
	static int totalnodes,colored,minc;
	static int c[],a[],n,parent[],ans[],size[];
	static long sum[];
	static HashMap<Integer,Integer> hm;
	public static void main(String[] args) throws IOException {
		
		Scanner sc=new Scanner(System.in);
		//in=new InputReader(System.in);
		out=new PrintWriter(System.out);
		double m=sc.nextDouble();
		double b=sc.nextDouble();
		double y=b;
		double x=(b*m);
		/*double midx=(double)(x)/2;double midy=(double)(y)/2;
		if(midx==Math.floor(midx) && midy==Math.floor(midy))
		{
			long ans=(long)(midx+1)*((long)(midy*(midy+1))/2);
			 ans+=(long)(midy+1)*((long)(midx*(midx+1))/2);
			out.println(ans);
		}
		else
		{
				
				int ans1=(int)((int)(midx/m)+1)*m;
				int ans2=-(ans1/m)+b;
				long ans=(long)(ans1+1)*((long)(ans2*(ans2+1))/2);
				 ans+=(long)(ans2+1)*((long)(ans1*(ans1+1))/2);
				out.println(ans);
			
			
		}
		*/
		long max=0;
		for(double i=y;i>=0.0;i--)
		{
			double x1=(b-i)*m;
			double ans=((x1+1.0))*((i*(i+1.0))/(2.0));
		//	double ans2=((i+1.0))*((x1*(x1+1.0))/(2.0));
			double ans3=(x1*((x1+1.0))/(2.0));
		double ans4=i+1.0;
			 long ans2=(long)(ans4)*(long)(ans3);
			 long p=(long)ans+(long)ans2;
			max=Math.max(max,p);
			
		}
		out.println(max);
		out.close();
		}
	static int check(int m)
	{
		int c=0;
		for(int i=0;i<n-1;i++)
		{
			int l=i;
			int r=n-1;
			while(l<r)
			{
				int mid=(l+r)/2;
				
				if(a[i]+m+1>a[mid])
					l=mid+1;
				else
					r=mid;
			}
		//debug(" l****** "+l);
			if(!(a[l]-a[i]<=m))
			while(a[l]==a[l-1])
				l--;
			
		//	debug((l-1-(i)));
			if(l==n-1 && !(a[l]-a[i]>m) )
				c=c+l-i;
			else
			c=c+(l-1-(i));
		}
		
		return c;
	}
	static InputReader in;
	static PrintWriter out;
 	static void dfs(int i)
	{
 		 size[i]=1;int badabeta=0;
 		 for(int j=0;j<adj[i].size();j++)
 		 {
 			 int son=adj[i].get(j);
 			 dfs(son);
 			 size[i]+=size[son];
 			 
 			 if(size[son]>size[badabeta])
 				 badabeta=son;
 		 }
 		 if(size[badabeta]*2>size[i])
 		 {
 			 int dada = ans[badabeta];
 			 while((size[i]-size[dada])*2>size[i])
 				 dada=parent[dada];
 			 ans[i]=dada;
 		 }
		
	}
	/*public static void seive(long n){
		b = new boolean[(int) (n+1)];
	Arrays.fill(b, true);
	
		for(int i = 2;i*i<=n;i++){
			if(b[i]){
				sum[i]=count[i];
			//	System.out.println(sum[i]+" wf");
				for(int p = 2*i;p<=n;p+=i){
					b[p] = false;
					sum[i]+=count[p];  
					//System.out.println(sum[i]);
				}
			}
		
		}
	}*/
	static class Pair implements Comparable<Pair> {
		int i;
		int j;
		//int index;
		public Pair(){
			
		}
		public Pair(int u, int v) {
			this.i = u;
			this.j= v;
			
		}
		public int compareTo(Pair other) {
			
			
				return this.j-other.j;
		}
		
		/*public String toString() {
			return "[u=" + u + ", v=" + v + "]";
		}*/
	}
	static class Node2{
		Node2 left = null;
		Node2 right = null;
		Node2 parent = null;
		int data;
	}
	
	//binaryStree
	static class BinarySearchTree{
		Node2 root = null;
		int height = 0;
		int max = 0;
		int cnt = 1;
		ArrayList<Integer> parent = new ArrayList<>();
		HashMap<Integer, Integer> hm = new HashMap<>();
		public void insert(int x){
			Node2 n = new Node2();
			n.data = x;
			if(root==null){
				root = n;
			}
			else{
				Node2 temp = root,temp2 = null;
				while(temp!=null){
					temp2 = temp;
					if(x>temp.data) temp = temp.right;
					else temp = temp.left;
				}
				if(x>temp2.data) temp2.right = n;
				else temp2.left = n;
				n.parent = temp2;
				parent.add(temp2.data);
			}
		}
		public Node2 getSomething(int x, int y, Node2 n){
			if(n.data==x || n.data==y) return n;
			else if(n.data>x && n.data<y) return n;
			else if(n.data<x && n.data<y) return getSomething(x,y,n.right);
			else return getSomething(x,y,n.left);
		}
		public Node2 search(int x,Node2 n){
			if(x==n.data){
				max = Math.max(max, n.data);
				return n;
			}
			if(x>n.data){
				max = Math.max(max, n.data);
				return search(x,n.right);
			}
			else{
				max = Math.max(max, n.data);
				return search(x,n.left);
			}
		}
		public int getHeight(Node2 n){
			if(n==null) return 0;
			height = 1+ Math.max(getHeight(n.left), getHeight(n.right));
			return height;
		}
	}
public static void debug(Object... o) {
	System.out.println(Arrays.deepToString(o));
}

public static String rev(String s)
{
	StringBuilder sb=new StringBuilder(s);
	sb.reverse();
	return sb.toString();
}

static long lcm(long a, long b)
{
    return a * (b / gcd(a, b));
}

static long gcd(long a, long b)
{
    while (b > 0)
    {
        long temp = b;
        b = a % b; // % is remainder
        a = temp;
    }
    return a;
}

public static long max(long x, long y, long z){
		if(x>=y && x>=z) return x;
		if(y>=x && y>=z) return y;
		return z;
	}
	static int[] sieve(int n,int[] arr)
	{
	for(int i=2;i*i<=n;i++)
	{
		if(arr[i]==0)
		{
			for(int j=i*2;j<=n;j+=i)
				arr[j]=1;
		}
	}
	return arr;
	}




static class InputReader {

private final InputStream stream;
private final byte[] buf = new byte[8192];
private int curChar, snumChars;
private SpaceCharFilter filter;

public InputReader(InputStream stream) {
  this.stream = stream;
}

public int snext() {
  if (snumChars == -1)
    throw new InputMismatchException();
  if (curChar >= snumChars) {
    curChar = 0;
    try {
      snumChars = stream.read(buf);
    } catch (IOException e) {
      throw new InputMismatchException();
    }
    if (snumChars <= 0)
      return -1;
  }
  return buf[curChar++];
}

public int nextInt() {
  int c = snext();
  while (isSpaceChar(c)) {
    c = snext();
  }
  int sgn = 1;
  if (c == '-') {
    sgn = -1;
    c = snext();
  }
  int res = 0;
  do {
    if (c < '0' || c > '9')
      throw new InputMismatchException();
    res *= 10;
    res += c - '0';
    c = snext();
  } while (!isSpaceChar(c));
  return res * sgn;
}

public long nextLong() {
  int c = snext();
  while (isSpaceChar(c)) {
    c = snext();
  }
  int sgn = 1;
  if (c == '-') {
    sgn = -1;
    c = snext();
  }
  long res = 0;
  do {
    if (c < '0' || c > '9')
      throw new InputMismatchException();
    res *= 10;
    res += c - '0';
    c = snext();
  } while (!isSpaceChar(c));
  return res * sgn;
}

public int[] nextIntArray(int n) {
	 return nextIntArray(n, 0);
	    }
	    
public int[] nextIntArray(int n, int off) {
	 int[] arr = new int[n + off];
	   for (int i = 0; i < n; i++) {
	    arr[i + off] = nextInt();
	    }
	    return arr;
	    }
	    
public long[] nextLongArray(int n) {
return nextLongArray(n, 0);
	    }
        
	public long[] nextLongArray(int n, int off) {
	 long[] arr = new long[n + off];
	 for (int i = 0; i < n; i++) {
		  arr[i + off] = nextLong();
		 }
 return arr;
	}


public String readString() {
  int c = snext();
  while (isSpaceChar(c)) {
    c = snext();
  }
  StringBuilder res = new StringBuilder();
  do {
    res.appendCodePoint(c);
    c = snext();
  } while (!isSpaceChar(c));
  return res.toString();
}

public String nextLine() {
  int c = snext();
  while (isSpaceChar(c))
    c = snext();
  StringBuilder res = new StringBuilder();
  do {
    res.appendCodePoint(c);
    c = snext();
  } while (!isEndOfLine(c));
  return res.toString();
}

public boolean isSpaceChar(int c) {
  if (filter != null)
    return filter.isSpaceChar(c);
  return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
}

private boolean isEndOfLine(int c) {
  return c == '\n' || c == '\r' || c == -1;
}

public interface SpaceCharFilter {
  public boolean isSpaceChar(int ch);
}
}
	
}