System Call

Operating systems in the Unix family provide a system call named read() for reading files. When passed a buffer of $K$ bytes, read() loads file contents into that buffer, and one call takes $(T + K)$ time, where $T$ is the fixed per-call overhead. The running time depends only on the buffer size, never on how many bytes are actually read. For example, with a 10-byte buffer, reading 3 bytes and reading 7 bytes both take $(T + 10)$ time.

Reading a single file of $F$ bytes therefore needs $\lceil F / K \rceil$ calls. The total time to read all of $N$ files with sizes $F_1, F_2, \dots, F_N$ bytes is

$\sum_{i=1}^{N} \lceil F_i / K \rceil \times (T + K)$

Mingyu decided to use one fixed buffer size $K$ for every file, where $K$ is a positive integer. Find the buffer size $K$ that minimizes the total reading time.

The first line contains the number of files $N$. The second line contains $N$ positive integers $F_i$, the file sizes in bytes. The third line contains the fixed per-call time $T$, a nonnegative integer.

Print the shortest achievable total reading time and the buffer size $K$ attaining it, separated by a space. If several buffer sizes achieve the shortest time, print the smallest such $K$.

Linux is a representative Unix-family operating system. macOS also belongs to the Unix family, along with FreeBSD, NetBSD, Solaris, and others.