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]. 
''' Hey stalker :) '''
INF = 10**10
def main():
    #print = out.append
    ''' Cook your dish here! '''
    n, m = get_list()
    P = 10**9 + 7
    dp = [[1]*m for _ in range(n)]
    for j in range(1, m):
        for i in range(1, n):
            dp[i][j] = (dp[i-1][j] + dp[i][j-1])%P
    #print(dp)
    k = 0
    res = 0
    for i in range(n):
        k = (k + dp[i][-1])%P
        res = (res + (k*dp[n-i-1][-1])%P)%P
    print(res)



''' Pythonista fLite 1.1 '''
import sys
#from collections import defaultdict, Counter
#from functools import reduce
import math
#input = iter(sys.stdin.buffer.read().decode().splitlines()).__next__
out = []
get_int = lambda: int(input())
get_list = lambda: list(map(int, input().split()))
main()
#[main() for _ in range(int(input()))]
#print(*out, sep='\n')


