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 inbuilt standard input output  
from sys import stdin, stdout

combi = dict()
dp = dict()
dp2 = dict()
def cal_dp(N,M):
    dp[(0,M)] = 1
    for i in range(1, N):
        dp[(i,M)] = dp[(i-1,M)] + combi[(i,M)]
    dp2[(0,M)] = 1
    for i in range (1, N):
        dp2[(i,M)] = dp2[(i-1,M)] + dp[(i,M)]

def calculate(N, M):
    if (N == 0):
        return 1
    if (N - 1, M) in combi:
        return combi[(N - 1,M)]
    sums = 0
    
    for i in range(1, N + 1):
        if i==1:
            for j in range(N, i -1, -1):
                sums = (sums + calculate(j - i + 1, M-1))
            if (N-1,M-1) not in dp:
                cal_dp(N,M-1)
        else:
            sums = (sums + dp2[(N - i, M -1)])
            break
    sums = sums % 1000000007
    combi[(N - 1,M)] = sums
    return sums

def main():
    arr = list(map(int, stdin.readline().split()))
    N = arr[0]
    M = arr[1]
    # prepare sums
    sums = 0
    for i in range(0, N):
        sums = (sums + i + 1 )% 1000000007
        combi[(i, 1)] = sums 
    combi[(i+1, 1)] = sums
    print(calculate(N, M))
main()