def grid_move(rights, ups):
    pre_row = []
    pre_row.append(0)
    # initialize for zero right and up only
    for i in range(1, ups+1):
        pre_row.append(1)
    cur_row = []
    for r in range(1, rights+1):
        for u in range(0, ups+1):
            if u > 0:
                cur_row.append(pre_row[u] + cur_row[-1])
            else:
                cur_row.append(1)
        pre_row = cur_row

    return cur_row[-1]

if __name__ == "__main__":
    print grid_move(2,3)