Lipshitz Sequence

1000ms

262144K

Description:

A function $\text{[math]}$ is called Lipschitz continuous if there is a real constant K such that the inequality |f(x) - f(y)| ≤ K·|x - y| holds for all $\text{[math]}$ . We'll deal with a more... discrete version of this term.

For an array $\text{[math]}$ , we define it's Lipschitz constant $\text{[math]}$ as follows:

if n < 2, $\text{[math]}$
if n ≥ 2, $\text{[math]}$ over all 1 ≤ i < j ≤ n

In other words, $\text{[math]}$ is the smallest non-negative integer such that |h[i] - h[j]| ≤ L·|i - j| holds for all 1 ≤ i, j ≤ n.

You are given an array $\text{[math]}$ of size n and q queries of the form [l, r]. For each query, consider the subarray $\text{[math]}$ ; determine the sum of Lipschitz constants of all subarrays of $\text{[math]}$ .

Input:

The first line of the input contains two space-separated integers n and q (2 ≤ n ≤ 100 000 and 1 ≤ q ≤ 100) — the number of elements in array $\text{[math]}$ and the number of queries respectively.

The second line contains n space-separated integers $\text{[math]}$ ( $\text{[math]}$ ).

The following q lines describe queries. The i-th of those lines contains two space-separated integers l_i and r_i (1 ≤ l_i < r_i ≤ n).

Output:

Print the answers to all queries in the order in which they are given in the input. For the i-th query, print one line containing a single integer — the sum of Lipschitz constants of all subarrays of $\text{[math]}$ .

Sample Input:

10 4
1 5 2 9 1 3 4 2 1 7
2 4
3 8
7 10
1 9

Sample Output:

Sample Input:

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

Sample Output:

Note:

In the first query of the first sample, the Lipschitz constants of subarrays of $\text{[math]}$ with length at least 2 are:

$\text{[math]}$
$\text{[math]}$
$\text{[math]}$

The answer to the query is their sum.

Informação

Provedor Codeforces

Código CF601B