Maximum Frequency After Subarray Operation

Choose one contiguous subarray and add the same integer x to every element once to maximize how many elements equal k afterward. Algorithmically, this is equivalent to picking a source value v = k - x and finding a contiguous interval that converts the most v's into k (without turning existing k's into something else), under constraints n ≤ 1e5 and nums[i], k ≤ 50.