You're given an array, and you can update elements in that array by performing integer division with divisor d. What is the minimum number of divisions needed so that there are T numbers that are the same in the array.

E.g. [1,2,3,4,5], threshold T = 3, d = 2. We want the min number of divisions needed so that 3 numbers are the same in the array. The answer is 2. We can divide 2 // 2 = 1 and 3 // 2 = 1 to get 3 1's with 2 operations, or 4 // 2 = 2 and 5 // 2 = 2 to get 3 2's. Another example is [16, 32, 64], T = 3, d = 2, answer is 3. 32 // 2 = 16, and 64 // 2 = 32, then 32 // 2 = 16, 3 divisions needed.

I tried taking the largest number and dividing that each time but when I realized it fails for cases like [1, 2, 10000000], T = 2, d = 2, I ran out of time.