King

A queen once gave birth to a son who would become king. Sadly, the prince could do very little arithmetic: he could only add integers and compare a sum against a single given integer bound. Moreover, the numbers he worked with had to be arranged in one sequence, and he could only add up contiguous parts of that sequence.

So that his son could rule after him, the old king decreed that every matter of state be presented as a finite sequence of integers, and every decision be made as an integer bound (an upper or lower limit) on the sum of that sequence.

After the old king died, the young king began to reign, and his decisions soon made him enemies. His opponents brought him a set of problems phrased as subsequences of a single integer sequence $S = \{a_1, a_2, \dots, a_n\}$. For each subsequence $S_i = \{a_{s_i}, a_{s_i+1}, \dots, a_{s_i+n_i}\}$ the king declared an integer bound $k_i$ on its sum, in one of the two forms

$a_{s_i} + a_{s_i+1} + \dots + a_{s_i+n_i} < k_i \qquad \text{or} \qquad a_{s_i} + a_{s_i+1} + \dots + a_{s_i+n_i} > k_i.$

Later the king realized that some of his declared bounds were mutually inconsistent. He cannot take back a declaration, but he can forge the underlying sequence. Help his advisors: decide whether there exists an integer sequence $S$ that satisfies all of the declared bounds.

The input consists of several blocks. Every block except the last describes one set of decisions.

The first line of a block contains two integers $n$ and $m$, where $0 < n \le 100$ is the length of the sequence $S$ and $0 < m \le 100$ is the number of bounds.

Each of the next $m$ lines contains one bound as four values $s_i\ n_i\ o_i\ k_i$:

• $s_i$ and $n_i$ select the subsequence $a_{s_i}, a_{s_i+1}, \dots, a_{s_i+n_i}$;
• $o_i$ is the comparison operator, given as gt for $>$ or lt for $<$;
• $k_i$ is the integer bound applied to the sum of that subsequence.

The last block is a single line containing 0 and must not be processed.

For each block, print one line:

• successful conspiracy if no integer sequence $S$ can satisfy all of the block's bounds;
• lamentable kingdom otherwise.

Print nothing for the final 0 block.