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.util.*;
import java.lang.*;
import java.io.*;

public class feb20 {

	public static void main(String[] srgs) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] scn = (br.readLine()).trim().split(" ");
		int n = Integer.parseInt(scn[0]);
		int m = Integer.parseInt(scn[1]);
		long[] fact = new long[n + 2 * m];
		fact[0] = 1;
		long mod = 1000000007l;
		for (int i = 1; i < fact.length; i++) {
			fact[i] = fact[i - 1] * i;
			fact[i] %= mod;
		}
		long ans = 0;
		// ncr ==== (n+2*m-1) C 2*m
		long a = pow(fact[2 * m], mod - 2, mod);
		long b = pow(fact[n - 1], mod - 2, mod);
		long c = fact[n + 2 * m - 1];
		ans = (((c * a) % mod) * b) % mod;
		System.out.println(ans);
		return;

	}

	public static long pow(long a, long x, long mod) {
		if (x == 0) {
			return 1l;
		}
		long p = pow(a, x / 2, mod);
		long ans = (p * p) % mod;
		if (x % 2 == 1) {
			ans = (ans * a) % mod;
		}
		return ans;
	}

	public static void sec() throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(br.readLine());
		StringBuilder sb = new StringBuilder();
		while (t-- > 0) {
			String[] scn = (br.readLine()).trim().split(" ");
			int n = Integer.parseInt(scn[0]);
			long[] arr = new long[n];
			scn = (br.readLine()).trim().split(" ");
			for (int i = 0; i < n; i++) {
				arr[i] = Long.parseLong(scn[i]);
			}
			sb.append("\n");
		}
		System.out.println(sb);
		return;

	}

	public static void third() throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringBuilder sb = new StringBuilder();
		String[] scn = (br.readLine()).trim().split(" ");
		int n = Integer.parseInt(scn[0]);
		long[] arr = new long[n];
		scn = (br.readLine()).trim().split(" ");
		for (int i = 0; i < n; i++) {
			arr[i] = Long.parseLong(scn[i]);
		}
		System.out.println(sb);
		return;

	}

	public static void debug() {
		System.out.println("working..");
	}

	public static void debug(int i) {
		System.out.println("working on " + i);
	}

	public static void sort(long[] arr) {
		int n = arr.length;
		for (int i = 0; i < n; i++) {
			int idx = (int) Math.random() * n;
			long temp = arr[i];
			arr[i] = arr[idx];
			arr[idx] = temp;
		}

		Arrays.sort(arr);
	}

	public static void sort(int[] arr) {
		int n = arr.length;
		for (int i = 0; i < n; i++) {
			int idx = (int) Math.random() * n;
			int temp = arr[i];
			arr[i] = arr[idx];
			arr[idx] = temp;
		}
		Arrays.sort(arr);
	}

	public static void print(long[][] dp) {
		for (long[] a : dp) {
			for (long ele : a) {
				System.out.print(ele + " ");
			}
			System.out.println();
		}
	}

	public static void print(int[][] dp) {
		for (int[] a : dp) {
			for (int ele : a) {
				System.out.print(ele + " ");
			}
			System.out.println();
		}
	}

	public static void print(boolean[] dp) {
		for (boolean ele : dp) {
			System.out.print(ele + " ");
		}
		System.out.println();
	}

	public static void print(long[] dp) {
		for (long ele : dp) {
			System.out.print(ele + " ");
		}
		System.out.println();
	}

}