Preparando MOJI

Two Arrays

1000ms 262144K

Description:

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 $$$10^9+7$$$.

Input:

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

Output:

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

Sample Input:

2 2

Sample Output:

5

Sample Input:

10 1

Sample Output:

55

Sample Input:

723 9

Sample Output:

157557417

Note:

In the first test there are $$$5$$$ suitable arrays:

  • $$$a = [1, 1], b = [2, 2]$$$;
  • $$$a = [1, 2], b = [2, 2]$$$;
  • $$$a = [2, 2], b = [2, 2]$$$;
  • $$$a = [1, 1], b = [2, 1]$$$;
  • $$$a = [1, 1], b = [1, 1]$$$.

Informação

Codeforces

Provedor Codeforces

Código CF1288C

Tags

combinatoricsdp

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Datas 09/05/2023 09:58:09

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