Compute the exact $\mathrm{Binomial}(n, p)$ probability of k successes, and the Poisson approximation to it with $\lambda = np$. Return the absolute difference.

The approximation is good when n is large and p small, and visibly poor when p is not small. Returning the error rather than either value makes that trade-off the answer.

Input

n = 1000
p = 0.001
k = 1

Output

0.0001840470877805811