Under the risk-neutral measure, a stock's price at expiry T is uniformly distributed on [a, b]. The continuously compounded risk-free rate is r.

Compute the price of the European call with strike K and expiry T.

Input

Five numbers a, b, K, r and T.

Output

One real number: the call price, with absolute or relative error at most 1e-9.

Constraints

0 <= a < b <= 10^4

0 <= K <= 1.5 * 10^4

-0.05 <= r <= 0.1

0.001 <= T <= 30

Scoring

This is a standard problem: a submission scores full points if it produces the correct output for every test case, and zero otherwise.

Numeric answers are accepted if they are within a relative tolerance of 1e-09 of the expected value.