Observe that for every valid `i`, the XOR of the subarray `nums[i..i+k-1]` must be `0`. This implies that `nums[i] ^ nums[i+1] ^ ... ^ nums[i+k-1] = 0`.

Notice that if `nums[i] ^ nums[i+k] = 0`, then `nums[i] = nums[i+k]`. This suggests that the array must be periodic with period `k` for the XOR condition to hold.

To minimize changes, identify the most frequent value in each "block" of size `k` (i.e., positions `i, i+k, i+2k, ...`). Changing all elements in a block to this most frequent value will minimize the number of changes for that block.