Balanced Lineup

For the daily milking, Farmer John's $N$ cows ($1 \le N \le 50{,}000$) always line up in the same order. One day Farmer John decides to organize a game of Ultimate Frisbee with some of the cows. To keep things simple, he takes a contiguous range of cows from the milking lineup to play the game. However, for all the cows to have fun, they should not differ too much in height.

Farmer John has made a list of $Q$ ($1 \le Q \le 200{,}000$) potential groups of cows and their heights ($1 \le \text{height} \le 1{,}000{,}000$). For each group, help him determine the difference in height between the shortest and the tallest cow in the group.

• Line 1: Two space-separated integers, $N$ and $Q$.
• Lines 2 to $N+1$: Line $i+1$ contains a single integer, the height of cow $i$.
• Lines $N+2$ to $N+Q+1$: Two integers $A$ and $B$ ($1 \le A \le B \le N$), representing the range of cows from $A$ to $B$ inclusive.

• Lines 1 to $Q$: Each line contains a single integer, the difference in height between the tallest and the shortest cow in the corresponding range.