Mad Scientist

A mad scientist performed a series of experiments, each consisting of $n$ phases. During each phase, a measurement was taken, resulting in a positive integer not exceeding $k$. The scientist knew that the measurements in each experiment were monotonically increasing, that is, each subsequent measurement was at least as large as the previous ones. For example, here is a sequence of measurements for one experiment with n=13 and k=6:

1, 1, 2, 2, 2, 2, 2, 4, 5, 5, 5, 5, 6

It was also known that $n$ was greater than $k$, so there were often many repeated values in the measurement sequence. Being mad, the scientist chose an unusual way to record the data. Rather than record each of the $n$ measurements, the scientist recorded a sequence $P$ of $k$ values defined as follows. For 1\leq j\leq k, $P(j)$ denotes the number of phases having a measurement of $j$ or less. For example, the original measurements from the above experiment were recorded as the $P$-sequence:

2, 7, 7, 8, 12, 13

as there were two measurements less than or equal to $1$, seven measurements less than or equal to $2$, seven measurements less than or equal to $3$, and so on.

Unfortunately, the scientist eventually went insane, leaving behind a notebook with these $P$-sequences for a series of experiments. Your job is to write a program that recovers the original measurements for the experiments.