Gerard the handyman

Gerard the handyman is a resourceful fellow. He loves to tinker with and repair his bike. Unfortunately, he has lost one of his precious tools: his ruler.

To compensate, he takes a bar of length 6 cm and marks two points on it, at 1 cm and 4 cm. With these marks, he can now measure any integer length from 1 to 6. Moreover, each measurement can be made in exactly one way:

Given a bar of length $n$ and $k$ marked points given in increasing order, please determine whether it is possible to measure all lengths from 1 to $n$ . Additionally, determine whether each measurable length can be obtained in a unique way or in multiple ways.

Input

Input consists of several cases, each one with $n$ and $k$ , followed by the positions $p_i$ of the points. Assume $2 \le n \le 1000$ , $1 \le k < n$ , and $1 \le p_1 < p_2 < \dots < p_k < n$ .

Output

For every case, print “YES” or “NO” followed by “unique” or “multiple”, depending on the answer.

Problem information

Author: Joan Alemany

Generation: 2026-01-25T11:06:06.427Z