You are given two integers n and m. Calculate the number of pairs of arrays (a, b) such that:

  * the length of both arrays is equal to m; 
  * each element of each array is an integer between 1 and n (inclusive); 
  * a_i ≤ b_i for any index i from 1 to m; 
  * array a is sorted in non-descending order; 
  * array b is sorted in non-ascending order. 



As the result can be very large, you should print it modulo 10^9+7.

Input

The only line contains two integers n and m (1 ≤ n ≤ 1000, 1 ≤ m ≤ 10).

Output

Print one integer – the number of arrays a and b satisfying the conditions described above modulo 10^9+7.

Examples

Input


2 2


Output


5


Input


10 1


Output


55


Input


723 9


Output


157557417

Note

In the first test there are 5 suitable arrays: 

  * a = [1, 1], b = [2, 2]; 
  * a = [1, 2], b = [2, 2]; 
  * a = [2, 2], b = [2, 2]; 
  * a = [1, 1], b = [2, 1]; 
  * a = [1, 1], b = [1, 1]. 
 
import java.io.*;
import java.math.BigInteger;
import java.util.*;
 
public class Main {
    static class FastReader
    {
        private InputStream mIs;private byte[] buf = new byte[1024];private int curChar,numChars;public FastReader() { this(System.in); }public FastReader(InputStream is) { mIs = is;}
        public int read() {if (numChars == -1) throw new InputMismatchException();if (curChar >= numChars) {curChar = 0;try { numChars = mIs.read(buf);} catch (IOException e) { throw new InputMismatchException();}if (numChars <= 0) return -1; }return buf[curChar++];}
        public String nextLine(){int c = read();while (isSpaceChar(c)) c = read();StringBuilder res = new StringBuilder();do {res.appendCodePoint(c);c = read();}while (!isEndOfLine(c));return res.toString() ;}
        public String next(){int c = read();while (isSpaceChar(c)) c = read();StringBuilder res = new StringBuilder();do {res.appendCodePoint(c);c = read();}while (!isSpaceChar(c));return res.toString();}
        public long l(){int c = read();while (isSpaceChar(c)) c = read();int sgn = 1;if (c == '-') { sgn = -1 ; c = read() ; }long res = 0; do{ if (c < '0' || c > '9') throw new InputMismatchException();res *= 10 ; res += c - '0' ; c = read();}while(!isSpaceChar(c));return res * sgn;}
        public int i(){int c = read() ;while (isSpaceChar(c)) c = read();int sgn = 1;if (c == '-') { sgn = -1 ; c = read() ; }int res = 0;do{if (c < '0' || c > '9') throw new InputMismatchException();res *= 10 ; res += c - '0' ; c = read() ;}while(!isSpaceChar(c));return res * sgn;}
        public double d() throws IOException {return Double.parseDouble(next()) ;}
        public boolean isSpaceChar(int c) { return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1; }
        public boolean isEndOfLine(int c) { return c == '\n' || c == '\r' || c == -1; }
        public void scanIntArr(int [] arr){ for(int li=0;li<arr.length;++li){ arr[li]=i();}}
        public void scanLongArr(long [] arr){for (int i=0;i<arr.length;++i){arr[i]=l();}}
        public void shuffle(int [] arr){ for(int i=arr.length;i>0;--i) { int r=(int)(Math.random()*i); int temp=arr[i-1]; arr[i-1]=arr[r]; arr[r]=temp; } }
    }
    public static void main(String[] args) throws IOException {
 
        FastReader fr=new FastReader();
        PrintWriter pw=new PrintWriter(System.out);
 
        /*
inputCopy
2 2
outputCopy
5
inputCopy
10 1
outputCopy
55
inputCopy
723 9
outputCopy
157557417
         */
        int t=1;
        for(int ti=0;ti<t;++ti) {
            int n=fr.i();
            int m=fr.i();
            //Its (2m+n-1)! / ((n-1)!*(2m)!)
            long mod=(long)(1e9+7);
            long num1=1;
            for(int i=2*m+n-1;i>=1;--i,num1%=mod)
                num1*=i;
            long divisor=1;
            for(int i=n-1;i>=1;--i,divisor%=mod)
                divisor*=i;
            for(int i=2*m;i>=1;--i,divisor%=mod)
                divisor*=i;
            BigInteger bigDiv=new BigInteger(divisor+"");
            BigInteger modInv=bigDiv.modInverse(new BigInteger(mod+""));
            long num2=modInv.longValue();
            pw.println((num1*num2)%mod);
        }
        pw.flush();
        pw.close();
    }
}