1288_C. Two Arrays
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]. 
```python
'''input
10 1
'''
# A coding delight
from sys import stdin, stdout
import gc
gc.disable()
input = stdin.readline
import math


# main starts
n, m = list(map(int, input().split()))
mod = 10 ** 9 + 7
dp1 = [[1 for x in range(m + 1)] for y in range(n + 1)]
dp2 = [[1 for y in range(m + 1)] for y in range(n + 1)]

for j in range(2, m + 1):
	for i in range(1, n + 1):
		temp = 0
		for k in range(1, i + 1):
			temp += dp1[k][j - 1]
			temp %= mod 
		dp1[i][j] = temp 		
		temp = 0
		for k in range(i, n + 1):
			temp += dp2[k][j - 1]
			temp %= mod
		dp2[i][j] = temp

# print(dp1)
# print(dp2)
ans = 0
for i in range(1, n + 1):
	for k in range(i, n + 1):
		ans += dp1[i][m] * dp2[k][m]
		ans %= mod 
print(ans)
```