Write a code in python given that n, t,a,v₀,x₀ will compute the estimate of x after t seconds.

where: n is the number of time slices per second (used to define t) t is the total number of seconds to be simulated a is the (constant) acceleration over the period v0 is the initial velocity x0 is the initial displacement

Let x_i and v_i represent the simulated values of x and v after i steps (x₀ and v₀ represent the initial displacement and velocity, respectively). Motion is simulated using the following update rules:

V_i +1 = V_{i +} a t

X_i +1 = X_i + V_i t

One line containing a space separated pair of integers representing the numerator and denominator of the estimate of x(t)presented as a rational number. (This way the value will be exact, and not subject to any round off errors). The numerator and denominator should be in their lowest terms.

Sample Input 0

5 2

3 1 4

Sample Output 0

57 5

Explanation 0

The given input indicates that t=1n=15 , x₀ =4 ,v₀ =1 and the acceleration is 3. We use the update rules to compute X_i and V_i for each value of i over the duration of 2 seconds. (Each second has been divided into n= 5 segments, so to simulate 2 seconds, we must compute the value of x₁₀ .)

Given the update rules, we can compute v₁ and x₁ from v₀ and x₀ respectively:

V₁ = v₀ + a t = 1+3 15=135= 85

x₁ = x₀ + v₀ t = 4+1 15=415= 215