Balloons
A rectangular field is composed of N rows and M columns, resulting in N·M cells. Each cell contains a ball, and all balls are uniquely colored, different from the color of the field itself.
In one move, you can take a ball from a cell located at (r, c) and place it in an adjacent cell (x, y). If there was a ball in cell (x, y), it is removed from the field.
Kostya, a boy, performed several such moves and then took a photograph of the field from above. When Kostya's father saw the photograph, he wondered how many different photographs could be taken from the initial field. This means considering the field filled with balls, performing a sequence of moves (possibly none), taking a photo, and then resetting the field to its original state to repeat the process for another photo. Kostya always takes the photographs in the same manner, without altering the camera's position, and the field itself remains stationary and unrotated. The entire field is visible in each photograph.
Input
The input consists of a single line with two integers N and M (1 ≤ N, M ≤ 50), representing the number of rows and columns of the field, respectively.
Output
Output a single line with the number of different photographs Kostya can take. Since this number can be very large, provide only the remainder when this number is divided by 1000200013.