Some ancillary operations that are often defined for binary min$-$heaps include DECREASEKEY$($p$,)$ and INCREASEKEY$($p$,)$ which decreases $($resp$.$ increases$)$ the key of the element at array$-$index p by some positive amount $,$ potentially causing the element to percolate up $($resp$.$ down$)$ in the heap.

$(15$ points$)$ Give pseudocode implementing DECREASEKEY.

$(15$ points$)$ Give pseudocode implementing$$ INCREASEKEY.