Problem: There are r red and g green blocks for construction of the red-green tower. Red-green tower can be built following next rules:

  * Red-green tower is consisting of some number of levels;

  * Let the red-green tower consist of n levels, then the first level of this tower should consist of n blocks, second level — of n - 1 blocks, the third one — of n - 2 blocks, and so on — the last level of such tower should consist of the one block. In other words, each successive level should contain one block less than the previous one;

  * Each level of the red-green tower should contain blocks of the same color.

<image>

Let h be the maximum possible number of levels of red-green tower, that can be built out of r red and g green blocks meeting the rules above. The task is to determine how many different red-green towers having h levels can be built out of the available blocks.

Two red-green towers are considered different if there exists some level, that consists of red blocks in the one tower and consists of green blocks in the other tower.

You are to write a program that will find the number of different red-green towers of height h modulo 109 + 7.

Input

The only line of input contains two integers r and g, separated by a single space — the number of available red and green blocks respectively (0 ≤ r, g ≤ 2·105, r + g ≥ 1).

Output

Output the only integer — the number of different possible red-green towers of height h modulo 109 + 7.

Examples

Input

4 6


Output

2


Input

9 7


Output

6


Input

1 1


Output

2

Note

The image in the problem statement shows all possible red-green towers for the first sample.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Main{
	InputStream is;
	static PrintWriter out;
	String INPUT = "";
	static long mod = (long)1e9+7L;
	
	public void solve(){
		int R = ni(), G = ni();
		int RG = R+G;
		int low = 1, high = 5000;
		while(low < high){
			int mid = low + (high - low + 1) / 2;
			int sum = (mid * (mid+1))/2;
			if(sum <= RG)low = mid;
			else high = mid-1;
		}

		int H = low;

		if(R>G){
			int tmp = G;
			G = R;
			R = tmp;
		}
		int tb = (H*(H+1))/2;
		long ans = 0L;
		long[] dp = new long[R+1];
		dp[0] = 1;

		for(int h = 1; h <= H; h++){
			long[] dc = new long[R+1];
			for(int i = 0; i <= R; i++){
				dc[i] = dp[i];
				if(i >= h)dc[i] = dc[i] + dp[i-h];
				if(dc[i] >= mod) dc[i] -= mod;
			}
			dp = dc;
		}

		for(int i = 0; i <= R; i++){
			if((tb-i) <= G){
				ans = ans + dp[i];
				if(ans >= mod)ans -= mod;
			}
		}
		out.println(ans);
	}
		/*dp = new long[Math.min(tb, R)+1][H+1];
		for(int i = 0; i <= Math.min(tb, R); i++)Arrays.fill(dp[i], -1);
		for(int i = Math.min(tb, R); i >= 0; i--){
			if(G+i < tb)break;
			ans = (ans + f(i, H))%mod;
		}

		out.println(ans);
	}
	long[][] dp;

	long f(int sum, int h){
		//out.println(sum+" "+h);
		if(dp[sum][h] != -1)return dp[sum][h];
		if(h == 0 && sum == 0)return dp[sum][h] = 1L;
		if(h == 0)return dp[sum][h] = 0L;

		dp[sum][h] = f(sum, h-1);
		if(sum >= h)dp[sum][h] = (dp[sum][h] + f(sum-h, h-1))%mod;
		return dp[sum][h];
	}
*/


	void run(){
		is = new DataInputStream(System.in);
		out = new PrintWriter(System.out);
		int t=1;while(t-->0)solve();
		out.flush();
	}
	public static void main(String[] args)throws Exception{new Main().run();}
	long mod(long v, long m){if(v<0){long q=(Math.abs(v)+m-1L)/m;v=v+q*m;}return v%m;}
    long mod(long v){if(v<0){long q=(Math.abs(v)+mod-1L)/mod;v=v+q*mod;}return v%mod;}
	//Fast I/O code is copied from uwi code.
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	private int readByte(){
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	private String ns(){
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	private char[] ns(int n){
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	private char[][] nm(int n, int m){
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	private int[] na(int n){
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	private int ni(){
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	private long nl(){
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	static  int i(long x){return (int)Math.round(x);}
	static class Pair implements Comparable<Pair>{
		long fs,sc;
		Pair(long a,long b){
			fs=a;sc=b;
		}
		public int compareTo(Pair p){
			if(this.fs>p.fs)return 1;
			else if(this.fs<p.fs)return -1;
			else{
				return i(this.sc-p.sc);
			}
			//return i(this.sc-p.sc);
		}
		public String toString(){
			return "("+fs+","+sc+")";
		}	
	}
	
}