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]. 
# Contest: Educational Codeforces Round 80 (Rated for Div. 2) (https://codeforces.com/contest/1288)
# Problem: C: Two Arrays (https://codeforces.com/contest/1288/problem/C)

def rint():
    return int(input())


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


f = [1]
for i in range(1, 20):
    f.append(i * f[-1])
def choose(n, k):
    return f[n] // f[n - k] // f[k]
n, m = rints()
M = 10**9 + 7
dp = [[0] * n for _ in range(m)]
dp[0] = [1] * n
for i in range(1, m):
    s = 0
    for j in range(n):
        s += dp[i-1][j]
        dp[i][j] = s
dpi = dp[-1]
dppref = [0] * n
dppref[0] = dpi[0]
for i in range(1, n):
    dppref[i] = dppref[i-1] + dpi[i]
p = 0
for i in range(n):
    p += dpi[i] * dppref[n - 1 - i]
print(p % M)
