Checkers on the cube

The surface of a cube is divided into square cells by lines parallel to the cube's edges. The side length of each cell is (l) (an odd natural number) times smaller than the edge length of the cube. A checker can move from one cell to any adjacent cell (sharing a side with the current one) in a single move.

Write a program to calculate the number of different ways the checker can travel, in exactly (m) moves, from the cell at the center of one face to the cell at the center of an adjacent face.

Input

The input consists of two natural numbers, (l) and (m), where (l < 52) and (m < 200).

Output

Output the number of possible ways.

Examples