**10 人解决**，13 人已尝试。

**14 份提交通过**，共有 22 份提交。

**5.2** EMB 奖励。

**单点时限: **1.0 sec

**内存限制: **256 MB

For the daily milking, Farmer John’s $N$ cows $(1 \leq N \leq 50~000)$ 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 will take 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 $Q$ $(1 \leq Q \leq 200~000)$ potential groups of cows and their heights $(1 \leq height \leq 1~000~000)$. For each group, he wants your help to 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 $2$..$N+1$: Line $i+1$ contains a single integer that is the height of cow $i$
- Lines $N+2$..$N+ Q+1$: Two integers $A$ and $B$ $(1 \leq A \leq B \leq N)$, representing the range of cows from $A$ to $B$ inclusive.

Lines $1$..$Q$: Each line contains a single integer that is a response to a reply and indicates the difference in height between the tallest and shortest cow in the range.

Input

6 3 1 7 3 4 2 5 1 5 4 6 2 2

Output

6 3 0

**10 人解决**，13 人已尝试。

**14 份提交通过**，共有 22 份提交。

**5.2** EMB 奖励。

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