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]. 
"""
NTC here
"""
import sys
input= sys.stdin.readline
flush= sys.stdout.flush
# import threading
# sys.setrecursionlimit(10**6)
# threading.stack_size(2**25)

def iin(): return int(input())
def lin(): return list(map(int, input().split()))

# range = xrange
# input = raw_input

def main():
    n, m=lin()
    md = 10**9+7
    a = list(range(1, n+1))
    a1 = [1]*n
    for i in range(m-1):
        a1 = a[:]
        for j in range(1, n):
            a[j] = (a[j]+a[j-1])% md
    ans = 0
    for i in range(n):
        ans += a1[i]*a[n-i-1]
        ans %= md
    print(ans)




        
main()
# threading.Thread(target=main).start()
