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]. 
#(a*b)%c=((a%c)*(b%c))%c
MOD=10**9+7

n,m=[int(x) for x in input().split()]

dp=[[0 for _ in range(2*m+1)] for __ in range(n+1)] #dp[i][j] is the no. of paths from [1][1] to [r][c]
dp[1][1]=1
for r in range(1,n+1):
    for c in range(1,2*m+1):
        if r>1:
            dp[r][c]+=dp[r-1][c]
        if c>1:
            dp[r][c]+=dp[r][c-1]
        dp[r][c]%=MOD

dp2=[0] #dp2[r] is the no. of paths from 1 to r inclusive
for i in range(1,n+1):
    dp2.append(dp[i][2*m-1]) #the 1st column must be fixed, so 1 column is subtracted

ans=0
cumu=0
counts=n

for endR in range(1,n+1):
#    print('endr:{} counts:{}'.format(endR,counts))
    ans+=dp2[endR]*counts
    ans%=MOD
    counts-=1

#print(dp2)
#print(p)
print(ans)