time limit per test: 0.25 sec.
memory limit per test: 65536 KB

input: standard
output: standard

A bishop is a piece used in the game of chess which is played on a board of square grids. A bishop can only move diagonally from its current position and two bishops attack each other if one is on the path of the other.

Given two numbers n and k, your job is to determine the number of ways one can put k bishops on an n × n chessboard so that no two of them are in attacking positions.

The input file contains two integers n (1 ≤ n ≤ 50) and k (0 ≤ k ≤ n²).

Print a line containing the total number of ways one can put the given number of bishops on a chessboard of the given size so that no two of them are in attacking positions.

Input

Test #1

4 4

Test #2

8 6