That's it. Sgt. Laugh has had enough. He is determined to end the evil military reign of General Cry. But Laugh isn't stupid. He knows, he needs a team to break through the walls of Cry.
Platoon "BattleCry'' has soldiers. Laugh will choose of these soldiers. The platoon is lined up. Height of the soldier is represented by . The sergeant wiil choose the soldiers in a way so that their heights form a strictly increasing sequence, i.e. if he chooses soldiers with indices where , condition must hold. Also since the sergeant is a little bit picky, the height difference between the tallest and shortest soldier must be minimum possible.
Help Laugh choose the squad.
First line of input contains two integers .
The following line contains integers representing the heights of the soldiers .
If no such squad could be formed, print on a line.
Otherwise, output the minimum possible difference between the tallest and shortest soldier in the chosen squad.
5 3 12 14 11 12 15
5 3 5 4 1 4 4