Product sum

There is a set of variables x_1, x_2, ..., x_N. Each variable x_i can be assigned the value -1, 0, +1 only. For a given integer p you are to calculate the number of ways variables x_i can be assigned values so that the sum of all possible products x_i·x_j is equal to S, where i < j and i, j = 1, 2, ..., N. Two ways are considered different if they contain a different number of x_i = 0.

Input

The input file contains two numbers: N and S, separated by space.

2 ≤ N ≤ 10000, -10000 < S < 10000.

Output

The output file should contains only one integer – the number of ways to represent S as a sum of products.

Examples