Let's consider a random permutation p_{1}, p_{2}, ..., p_{N} of numbers 1, 2, ..., N and calculate the value F=(X_{2}+...+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 <= 10^{9}

1 <= K <= 5

Sample input

1 1000

Sample Output

1996 / 3

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