Quality Tea

TLC have decided to start producing their own tea.

You have been asked to write a quality control program that monitors batches of products for faults.

A batch of $N$ products $(3 \le N \le 1000$) is considered to be faulty if it contains three consecutive defective products anywhere along the production line. A product is defective if its quality level $q_i$ is less than the quality threshold $K$ ($1 \le q_i, K \le 100$).

Your task is to determine whether the current batch of products is faulty or not.

Input

The first line will contain two space separated integers, $N$, the number of products in the current batch, and $K$, the quality threshold.

The next $N$ lines contain the quality levels of the current batch of products in order along the production line. Each quality level $q_i$ will be an integer on its own line.

Output

If the current batch of products is faulty, you should print Fault Detected on a single line. On the next line, print the first three consecutive quality levels which failed, separated by spaces.

Otherwise, print No Fault instead.

Subtasks

• Subtask 1 (40%) There will always be exactly three quality values to check ($N=3$ is guaranteed).
• Subtask 2 (60%) The full solution.