Kill Monsters (Hard Version)

**This is the hard version of the problem. Here, the values of $X$ and $K$ can go upto $10^9$, and $H_i$ can be as large as $10^{18}$.** In a video game, you are tasked with defeating monsters. The $i$-th monster has a health value of $H_i$. You start with an initial health value of $X$. You can defeat the $i$-th monster if your current health $X$ is **strictly greater than** the monster's h