For a certain program, $25\%$ of the instructions are $LW,10\%$ are $SW,45\%$ are $R,15\%$ are $B,5\%$ are J$.$ Consider the following three cases: $($i$)$ If there is no pipelining, the average time required for executing one instruction is $L($ns$).($ii$)$ If a $5-$stage pipeline is adopted, the average time required for executing one instruction in the ideal case is $M($ns$).($iii$)$ Assume that the destinations of Branch $($B$)$ and Jump $($J$)$ will not be known until the end of the ALU stage. If every $B$ or $J$ instruction incurs two pipeline bubbles, the average time required for executing one instruction is $N(ns).L+M+N=K.$ Then

$($a$)K<mn\; id="EditorElement\_401756">1</mn><mn\; id="EditorElement\_401757">3</mn>$

$($b$)13K<mn\; id="EditorElement\_401731">1</mn><mn\; id="EditorElement\_401732">4</mn>$

$($c$)14K<mn\; id="EditorElement\_401701">1</mn><mn\; id="EditorElement\_401702">5</mn>$

$($d$)15K<mn\; id="EditorElement\_401671">1</mn><mn\; id="EditorElement\_401672">6</mn>$

$($e$)16K.$

The following table shows the information about a machine executing instructions. There are $5$ classes of instructions, each of which takes $3-5$ steps.

$\backslash$table$[[$Instruction Class,Fetch,$\backslash$table$[[$Register$],[$Read$]],$ALU,$\backslash$table$[[$Memory$],[$access$]],\backslash$table$[[$Register$],[$Write$]]],[$Load Word $($LW$),2ns,,2ns,3ns,1ns$