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.Arrays;

public class Main {
    private final Reader reader;

    private final Writer writer;

    public static void main(String[] args) throws IOException {
        new Main().solve();

    }

    private void solve() throws IOException {
        int MOD = 1000000007;
        int R = reader.nextUnsignedInt();
        int G = reader.nextUnsignedInt();
        int H_MAX = 0;
        for (int h = 1; h < 10000; h++) {
            if ((h * (h + 1) / 2) > R + G) {
                H_MAX = h - 1;
                break;
            }
        }


        //dp[t][r] = dp[t-1][r-t] + dp[t-1][r];
        //dp[t][r] = number of towers of highest possible height H_MAX,
        //           that have t upper floor already coloured and we
        //           have used r red blocks to do so
        //answer will be dp[H_MAX][R];
        //
        int dp[][] = new int[2][R + 1];
        dp[0][0] = 1;

        for (int t = 1; t <= H_MAX; t++) {
            int now = t&1;
            int last = now^1;
            int coloured_blocks = t * (t - 1) / 2;
            for (int r = 0; r <= R; r++) {
                int redUsed = r;
                int greenUsed = coloured_blocks - redUsed;
                int greenRemaining = G - greenUsed;

                dp[now][r] = (r >= t && r <= (coloured_blocks + t) ? dp[last][r - t] : 0) //painting t level with t red blocks
                        + (greenRemaining >= t ? dp[last][r] : 0); // painting t level with t green blocks

                if (dp[now][r] >= MOD) {
                    dp[now][r] -= MOD;
                }
            }
        }

        int ans = 0;
        for (int r = 0; r <= R; r++) {
            ans = ans + dp[H_MAX&1][r];
            if (ans >= MOD) {
                ans -= MOD;
            }
        }
        writer.print(ans + "\n");
        writer.flush();
    }

    Main(InputStream in, OutputStream out) {
        this.reader = new Reader(in);
        this.writer = new Writer(out);
    }

    public Main() {
        this.reader = new Reader();
        this.writer = new Writer();
    }


}

class Reader {

    private final int BUFFER_SIZE = 65536;

    private final DataInputStream din;

    private final byte[] buffer;

    private int bufferPointer, bytesRead;

    Reader() {
        din = new DataInputStream(System.in);
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public Reader(InputStream in) {
        din = new DataInputStream(in);
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public long nextUnsignedLong() throws IOException {
        long ret = 0;
        byte c = read();
        while (c <= 32) c = read();
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0');
        return ret;
    }

    public int nextUnsignedInt() throws IOException {
        int ret = 0;
        byte c = read();
        while (c <= 32) c = read();
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0');
        return ret;
    }

    public int nextInt() throws IOException {
        int ret = 0;
        byte c = read();
        while (c <= ' ') c = read();
        boolean neg = (c == '-');
        if (neg) {
            c = read();
        }
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0');
        if (neg) {
            return -ret;
        }
        return ret;
    }

    public String nextString(int MAX) throws IOException {
        int cnt = 0;
        char[] buf = new char[MAX];
        byte c;
        while ((c = read()) < 33) ;
        buf[cnt++] = (char) c;
        while ((c = read()) >= 33) {
            buf[cnt++] = (char) c;
        }
        return new String(buf, 0, cnt);
    }

    public char firstCharOfNextUnSpacedString() throws IOException {
        byte c;
        char res;
        while ((c = read()) < 33) ;
        res = (char) c;
        while ((c = read()) >= 33) ;
        return res;
    }

    private void fillBuffer() throws IOException {
        bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
        if (bytesRead == -1) {
            buffer[0] = -1;
        }
    }

    private byte read() throws IOException {
        if (bufferPointer == bytesRead) {
            fillBuffer();
        }
        return buffer[bufferPointer++];
    }
}

class Writer {
    private final BufferedWriter out;

    Writer() {
        out = new BufferedWriter(new OutputStreamWriter(System.out), 512);
    }

    public Writer(OutputStream out) {
        this.out = new BufferedWriter(new OutputStreamWriter(out), 512);
    }

    void print(char c) throws IOException {
        out.write(c);
    }

    void print(String str) throws IOException {
        out.write(str);
    }

    void println() throws IOException {
        out.write("\n");
    }

    void flush() throws IOException {
        out.flush();
    }

    @Override
    protected void finalize() throws IOException {
        out.flush();
    }
}