Let's consider a random permutation p₁, p₂, ..., p_N of numbers 1, 2, ..., N and calculate the value F=(X₂+...+X_N-1)^K, where X_i equals 1 if one of the following two conditions holds: p_i-1 < p_i > p_i+1 or p_i-1 > p_i < p_i+1 and X_i equals 0 otherwise. What is the expected value of F?

Input Format:
The first line contains two integers K and N.

Output Format:
Print the expected value of F as an irreducible fraction p / q. Follow sample input for more clarification.

Constraints:
1000 <= N <= 10⁹
1 <= K <= 5

Sample input

1 1000

Sample Output

1996 / 3