Redundant ArrayChef has an array 𝐴A containing 𝑁N positive integers.He can perform the following operation on the array as many times as he likes:Choose integers 𝐿L and 𝑅R such that 1≤𝐿≤𝑅≤𝑁1≤L≤R≤N;Choose a positive integer 𝑥x;For every index 𝑖i from 𝐿L to 𝑅R (inclusive of both), set 𝐴𝑖=𝑥A i​ =x.The cost of such an operation is (𝑅−𝐿+1)⋅𝑥(R−L+1)⋅x.Find the minimum cost required to make all the elements of 𝐴A equal.Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case consists two lines of input.The first line of each test case contains a single integer 𝑁N — the size of the array.The second line contains 𝑁N space-separated integers 𝐴1,𝐴2,…,𝐴𝑁A 1​ ,A 2​ ,…,A N​ .Output FormatFor each test case, output on a new line the minimum cost needed to make all the elements of 𝐴A equal.Constraints1≤𝑇≤2×1051≤T≤2×10 5 1≤𝑁≤2×1051≤N≤2×10 5 1≤𝐴𝑖≤𝑁1≤A i​ ≤NThe sum of 𝑁N over all test cases does not exceed 2×1052×10 5 Sample 1:InputOutput352 4 3 2 233 3 371 3 7 5 1 4 3405

You are given an integer array nums and two integers cost1 and cost2. You are allowed to perform either of the following operations any number of times:Choose an index i from nums and increase nums[i] by 1 for a cost of cost1.Choose two different indices i, j, from nums and increase nums[i] and nums[j] by 1 for a cost of cost2.Return the minimum cost required to make all elements in the array equal.Since the answer may be very large, return it modulo 109 + 7. Example 1:Input: nums = [4,1], cost1 = 5, cost2 = 2Output: 15Explanation:The following operations can be performed to make the values equal:Increase nums[1] by 1 for a cost of 5. nums becomes [4,2].Increase nums[1] by 1 for a cost of 5. nums becomes [4,3].Increase nums[1] by 1 for a cost of 5. nums becomes [4,4].The total cost is 15.Example 2:Input: nums = [2,3,3,3,5], cost1 = 2, cost2 = 1Output: 6Explanation:The following operations can be performed to make the values equal:Increase nums[0] and nums[1] by 1 for a cost of 1. nums becomes [3,4,3,3,5].Increase nums[0] and nums[2] by 1 for a cost of 1. nums becomes [4,4,4,3,5].Increase nums[0] and nums[3] by 1 for a cost of 1. nums becomes [5,4,4,4,5].Increase nums[1] and nums[2] by 1 for a cost of 1. nums becomes [5,5,5,4,5].Increase nums[3] by 1 for a cost of 2. nums becomes [5,5,5,5,5].The total cost is 6.Example 3:Input: nums = [3,5,3], cost1 = 1, cost2 = 3Output: 4Explanation:The following operations can be performed to make the values equal:Increase nums[0] by 1 for a cost of 1. nums becomes [4,5,3].Increase nums[0] by 1 for a cost of 1. nums becomes [5,5,3].Increase nums[2] by 1 for a cost of 1. nums becomes [5,5,4].Increase nums[2] by 1 for a cost of 1. nums becomes [5,5,5].The total cost is 4. Constraints:1 <= nums.length <= 1051 <= nums[i] <= 1061 <= cost1 <= 1061 <= cost2 <= 106

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 an array of integers nums of length n.The cost of an array is the value of its first element. For example, the cost of [1,2,3] is 1 while the cost of [3,4,1] is 3.You need to divide nums into 3 disjoint contiguous subarrays.Return the minimum possible sum of the cost of these subarrays.

Geek and Geekina, the top students in their class, were vying for the leadership role. To determine the leader, their teacher assigned them arrays, arr1[] to Geek and arr2[] to Geekina of size n. The task was simple: calculate the cost of each array. The cost of the array is defined as the summing of VAL(a[i]) for each i in [0,n-1].VAL(x)=minimum number of operations to convert x to 0 or 1.In each operation, you can take any prime factor of the remaining value and subtract it from x.For example,  if we have 6, and if we subtract 3 from it, then our remaining value will become 3 and then we can not subtract 2 from it because 2 is not the prime factor of the current value of 3.Due to their busy schedules, Geek and Geekina have sought assistance in calculating the cost of their arrays. So your task is to return  1 if the cost of arr1 is less than or equal to the cost of arr2.  otherwise, it should return 0. Example 1:Input:n=3arr1={1,1,2}arr2={1,1,1}Output:0Explanation:VAL(1) is 0 and VAL(2) is 1 (2->0).Now Cost of arr1 is 1 and Cost of arr2 is 0.So 0 is the answer Cost(arr1)>Cost(arr2).

Make My Array EqualYou are given an array 𝐴A of length 𝑁N.Determine if it is possible to make all the elements of 𝐴A equal by performing the following operation any number of times (possibly, zero):Choose two distinct indices 𝑖i and 𝑗j (1≤𝑖,𝑗≤𝑁1≤i,j≤N, 𝑖≠𝑗i=j); andUpdate the value at index 𝑖i by setting 𝐴𝑖A i​ to 𝐴𝑖+𝐴𝑗A i​ +A j​ .For example, if 𝐴=[1,5,3,5,6]A=[1,5,3,5,6],Choosing 𝑖=5i=5 and 𝑗=3j=3 would result in the array [1,5,3,5,9][1,5,3,5,9], since we replace 𝐴5A 5​ with 𝐴5+𝐴3=9A 5​ +A 3​ =9.Choosing 𝑖=2i=2 and 𝑗=4j=4 would instead result in the array [1,10,3,5,6][1,10,3,5,6].Output "YES" if it is possible to make all elements of the array equal after performing several (possibly, zero) of these operations, otherwise output "NO" (without quotes).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 a single integer 𝑁N — the length of array.The second line of each test case contains 𝑁N space-separated integers 𝐴1,𝐴2,…,𝐴𝑁A 1​ ,A 2​ ,…,A N​ , denoting the initial array.Output FormatFor each test case, print Yes if it is possible to make all elements of array equal using any number of operations, otherwise print No.You may print each character of the output in either uppercase or lowercase (for example, the strings YES, yEs, yes, and yeS will all be treated as identical).Constraints1≤𝑇≤1051≤T≤10 5 1≤𝑁≤2⋅1051≤N≤2⋅10 5 0≤𝐴𝑖≤1090≤A i​ ≤10 9 The sum of 𝑁N over all test cases won't exceed 2⋅1052⋅10 5 .Sample 1:InputOutput331 1 121 231 0 0YESNOYES