P14602 [NWRRC 2025] Compact Encoding

Binary formats often use compact representations for integers. Consider writing a 32-bit unsigned integer to a file: you must always reserve 4 bytes to represent it (remember, 8 bits make one byte). However, in many real-life applications, integer values tend to be small. Writing these small values using a fixed 4-byte representation results in files that are mostly filled with zero bytes. To make the representation more compact, we introduce the following encoding scheme. Each value is represented as a sequence of bytes $b_1, b_2, \ldots, b_k$, where each $b_i$ is an integer between $0$ and $255$, inclusive. The most significant bit of each byte serves as a continuation flag, and the lower $7$ bits carry the actual data. If the continuation flag is $1$, more bytes follow; for the last byte, it is $0$. The representation is $\textit{big-endian}$, meaning that $b_1$ contains the most significant bits of the encoded value. For example, here's how to find the compact representation of $n = 112025$. First, we find its binary representation: $$112025 = 11011010110011001_2$$ Next, we split it into 7-bit chunks, padding with zeros on the left if necessary: :::align{center} $0000110$ / $1101011$ / $0011001$ ::: The first two chunks have a following chunk, so the corresponding bytes have their most significant bit set to $1$. The last chunk has no following chunk, so its most significant bit is $0$. This gives us: $$\begin{array}{l} b_1 = 10000110_2 = 134\\ b_2 = 11101011_2 = 235\\ b_3 = 00011001_2 = 25\\ \end{array}$$ You are given an integer $n$, and your task is to find its compact representation.

The only line contains a single integer $n$ ($0 \le n \le 2^{31}-1$).

Print a sequence of integers between $0$ and $255$, inclusive, representing the compact encoding of $n$. The encoding must not contain leading bytes with zero data bits: that is, it may not start with $128$.