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]. 
# -*- coding: utf-8 -*-

import math
import collections
import bisect
import heapq
import time
import random
import itertools
import sys
from typing import List

"""
created by shhuan at 2020/1/14 22:56

"""


def solve(N, M):
    MOD = 10 ** 9 + 7
    dp = [[0 for _ in range(N+1)] for _ in range(1 + M)]
    for v in range(1, N+1):
        dp[1][v] = 1
    for i in range(2, M+1):
        for v in range(1, N+1):
            dp[i][v] = sum([dp[i-1][u] for u in range(1, v+1)])
            dp[i][v] %= MOD

    dp2 = [[0 for _ in range(N+1)] for _ in range(1 + M)]
    for v in range(1, N+1):
        dp2[1][v] = 1
    for i in range(2, M+1):
        for v in range(1, N+1):
            dp2[i][v] = sum([dp2[i-1][u] for u in range(v, N+1)])
            dp2[i][v] %= MOD

    ans = 0
    for v in range(1, N+1):
        ans += sum([dp[M][v] * dp2[M][u] for u in range(v, N+1)])
        ans %= MOD

    return ans


N, M = map(int, input().split())
print(solve(N, M))