CF1288C 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 \le 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 $ .

The only line contains two integers $ n $ and $ m $ ( $ 1 \le n \le 1000 $ , $ 1 \le m \le 10 $ ).

Print one integer – the number of arrays $ a $ and $ b $ satisfying the conditions described above modulo $ 10^9+7 $ .

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] $ .