Code in java, please also show the correct output in the terminal, also look your code performance and make it more efficient You have M square tiles of size $1\backslash$times $1$ and N square tiles of size $2\backslash$times $2.$ Your task is to create the largest possible square using these tiles. Tiles may not over and the resulting square should be filled $($it should not contain empty spaces$).$ Write a function:

class Solution $\{$ public int solution$($int M $,$ int N $)$; $\}$

that, given two integers M and N$,$ returns the length of the side of the largest square you can create. If no square can be created, your function should return $0.$ Examples: $1.$ Given M$=8$ and N$=0,$ your function should return $2.$ You can use four out of eight tiles to arrange them into $2\backslash$times $2$ square. There are enough tiles to creat $3\backslash$times $3$ square. $2.$ Given M$=4$ and N$=3,$ your function should return $4.$ You can obtain a $4\backslash$times $4$ square by arranging four $1\backslash$times $1$ tiles into a $2\backslash$times $2$ square, and surrounding it by $2\backslash$times $2$ tiles: $3.$ Given M$=0$ and N$=18,$ your function should return $8.$ You need to use sixteen $2\backslash$times $2$ tiles to create the square. Note that not all the tiles are used. $4.$ Given M$=13$ and N$=3,$ your function should return $5.$ One of the possible arrangements is shown in the following image:Write an efficient algorithm for the following assumptions: $-$ M and N are integers within the range $[0.\mathrm{.}1,000,000,000].$