Two arrays#11725
You are given two positive integers and . Find the number of pairs of arrays that satisfy the following conditions:
Both arrays have a length of .
Each element of both arrays is an integer from to inclusive.
For every index from to , a_i \le b_i.
Array is sorted in non-decreasing order.
Array is sorted in non-increasing order.
Since the result may be very large, output it modulo 10^9 + 7.
Two positive integers and (1 \le n \le 1000,\ 1 \le m \le 10).
Print a single integer: the number of pairs of arrays and that satisfy the conditions above, modulo 10^9 + 7.
Example
2 25Example 1
Example 2
In the first sample test, there are suitable pairs:
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].