Shubhendu and his sister Priyanka went to a restaurant to treat themselves with delicious chicken after winning Badminton League of the Institute. Seeing her sister Priyanka getting bored waiting for the order , Shubhendu ask her to play a game. If Priyanka wins the game she will be allowed to order anything as per her wish.
The game consists of nXm matrix having n rows and n columns. There are two types of coin, one cross marked coin and other Circle marked coin. Cross marked coin is with Priyanka and circle marked coin is with Shubhendu.
Priyanka places her coin at the top row and Shubhendu places his coin at the bottom row. Both the coins at random column. Since he loves his sister very much ,he asked Priyanka to start the game. Priyanka can move her cross marked coin to any of the 8 directions in the matrix while Shubhendu can move either left or right or stay at the same position. Priyanka's aim is to catch Shubhendu's coin in minimum number of moves while Shubhendu has to survive as long as possible.
Help Priyanka to find what is the expected number of chances she has to move to win the game .
Note: Coin will be placed at some random column and corresponding rows i.e cross coin in first row and circle coin at last row. Movement of coins outside the grid is prohibited. Both of them will play the game optimally.
Input
Two integers n,m denoting number of rows and number of columns respectively.
Output
Print the desired output in the form of a/b i.e the desired expectation should be printed in the reduced fraction form.
Constraints
2 <= m,n <= 6000
For 2 rows and 2 columns , Priyanka's cross marked coin will be in first row and Shubhendu's Circle marked coin will be at last row i.e Second row. Suppose (a,b) denotes column number for Cross marked coin and cicle marked coin respectively.
(1,1) (1,2) (2,1) (2,2) are the possible column numbers . All are at a distance of one to catch. So the expected value will be (1+1+1+1)/4 =4/4 which in reduced form will be output as 1/1.
