K-ClosenessYou are given an array 𝐴A of length 𝑁N, and an integer 𝐾K.You can perform the following operation:Choose any index 𝑖i (1≤𝑖≤𝑁1≤i≤N), and increase 𝐴𝑖A i​ by 𝐾K.Find the minimum possible value of max⁡(𝐴)−min⁡(𝐴)max(A)−min(A) attainable, if you can perform this operation as many times as you like (possibly, zero times).Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case consists of two lines of input.The first line of each test case contains two space-separated integers 𝑁N and 𝐾K — the length of the array and the parameter 𝐾K.The second line contains 𝑁N space-separated integers 𝐴1,𝐴2,…,𝐴𝑁A 1​ ,A 2​ ,…,A N​ — the initial values of the array elements.Output FormatFor each test case, output on a new line the answer: the minimum possible value of max⁡(𝐴)−min⁡(𝐴)max(A)−min(A) if you can perform the given operation any number of times.Constraints1≤𝑇≤1051≤T≤10 5 1≤𝑁≤2⋅1051≤N≤2⋅10 5 1≤𝐾≤1091≤K≤10 9 1≤𝐴𝑖≤1091≤A i​ ≤10 9 The sum of 𝑁N over all test cases won't exceed 2⋅1052⋅10 5 .Sample 1:InputOutput43 41 5 43 212 8 44 11 43 62 8256 121 2 4 128 130 1311008Explanation:Test case 11: Increase the first element by 𝐾=4K=4 to obtain the array [5,5,4][5,5,4].Here, max⁡−min⁡=5−4=1max−min=5−4=1, which is the best possible.Test case 22: The second and third elements can be increased by 22 till they reach 1212, at which point all the elements of the array are equal, so max⁡(𝐴)−min⁡(𝐴)=0max(A)−min(A)=0.Test case 33: Since 𝐾=1K=1, again it's possible to make all the elements equal.Test case 44: Do the following:Increase 𝐴1A 1​ by 1212 repeatedly to make it 133133.Increase 𝐴2A 2​ by 1212 repeatedly to make it 134134.Increase 𝐴3A 3​ by 1212 repeatedly to make it 136136.The array is now [133,134,136,128,130,131][133,134,136,128,130,131].For this array, max⁡(𝐴)−min⁡(𝐴)=136−128=8max(A)−min(A)=136−128=8.It can be shown that this is optimal.

You are given an array 𝐴A of length 𝑁N, and an integer 𝐾K.You can perform the following operation:Choose any index 𝑖i (1≤𝑖≤𝑁1≤i≤N), and increase 𝐴𝑖A i​ by 𝐾K.Find the minimum possible value of max⁡(𝐴)−min⁡(𝐴)max(A)−min(A) attainable, if you can perform this operation as many times as you like (possibly, zero times).Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case consists of two lines of input.The first line of each test case contains two space-separated integers 𝑁N and 𝐾K — the length of the array and the parameter 𝐾K.The second line contains 𝑁N space-separated integers 𝐴1,𝐴2,…,𝐴𝑁A 1​ ,A 2​ ,…,A N​ — the initial values of the array elements.Output FormatFor each test case, output on a new line the answer: the minimum possible value of max⁡(𝐴)−min⁡(𝐴)max(A)−min(A) if you can perform the given operation any number of times.Constraints1≤𝑇≤1051≤T≤10 5 1≤𝑁≤2⋅1051≤N≤2⋅10 5 1≤𝐾≤1091≤K≤10 9 1≤𝐴𝑖≤1091≤A i​ ≤10 9 The sum of 𝑁N over all test cases won't exceed 2⋅1052⋅10 5 .Sample 1:InputOutput43 41 5 43 212 8 44 11 43 62 8256 121 2 4 128 130 1311008Explanation:Test case 11: Increase the first element by 𝐾=4K=4 to obtain the array [5,5,4][5,5,4].Here, max⁡−min⁡=5−4=1max−min=5−4=1, which is the best possible.Test case 22: The second and third elements can be increased by 22 till they reach 1212, at which point all the elements of the array are equal, so max⁡(𝐴)−min⁡(𝐴)=0max(A)−min(A)=0.Test case 33: Since 𝐾=1K=1, again it's possible to make all the elements equal.Test case 44: Do the following:Increase 𝐴1A 1​ by 1212 repeatedly to make it 133133.Increase 𝐴2A 2​ by 1212 repeatedly to make it 134134.Increase 𝐴3A 3​ by 1212 repeatedly to make it 136136.The array is now [133,134,136,128,130,131][133,134,136,128,130,131].For this array, max⁡(𝐴)−min⁡(𝐴)=136−128=8max(A)−min(A)=136−128=8.It can be shown that this is optimal.

You are given a 0-indexed integer array nums and an integer k. You have a starting score of 0.In one operation:choose an index i such that 0 <= i < nums.length,increase your score by nums[i], andreplace nums[i] with ceil(nums[i] / 3).Return the maximum possible score you can attain after applying exactly k operations.

Distinct Elements in WindowMax Score: 100Given an array of integers and a window size K, find the number of distinct elements in every window of size K of the given array.Input FormatThe first line of input contains T - the number of test cases. It's followed by 2T lines. The first line of each test case contains the N-size of the array and the K-size of the window. The second line contains N integers - elements of the array.Output FormatFor each test case, print the number of distinct elements in every window of size K, separated by a new line.Constraints30 points1 <= N <= 1001 <= K <= N70 points1 <= N <= 100001 <= K <= NGeneral Constraints1 <= T <= 1000-100 <= ar[i] <= 100ExampleInput35 3-2 -4 -2 4 -210 73 -4 -3 -4 -2 0 2 -2 6 017 13-5 -1 4 8 -5 -3 -4 7 4 -4 0 8 0 -2 3 2 5Output2 3 26 5 6 58 9 9 10 11ExplanationSelf Explanatory

Given an array of integers A, and an integer K find number of happy elements.Element X is happy if there exists at least 1 element whose difference is less than K i.e. an element X is happy if there is another element in the range [X-K, X+K] other than X itself.Constraints1 <= N <= 10^50 <= K <= 10^50 <= A[i] <= 10^9InputFirst line contains two integers N and K where N is size of the array and K is a number as described above. Second line contains N integers separated by space.OutputPrint a single integer denoting the total number of happy elements.ExampleInput3 21 3 5Output3ExplanationAll numbers have at least 1 element in the range [X-2, X+2]. Hence they are all happy elements. Since these three are in number, the output is 3.

You are given an integer array and an integer K. You have to tell if there exists a pair of integers in the given array such that ar[i]-ar[j]=K and i≠j.Input FormatThe first line of input contains T - the number of test cases. It's followed by 2T lines, the first line contains N and K - the size of the array and the number K. The second line contains the elements of the array.Output FormatFor each test case, print "true" if the arrays contains such elements, "false" otherwise, separated by new line.Constraints40 points2 <= N <= 100060 points2 <= N <= 100000General Constraints1 <= T <= 100-105 <= ar[i], K <= 105ExampleInput25 601 20 40 100 8010 1112 45 52 65 21 645 234 14 575 112Outputtruefalse